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LAMONT GEOLOGICAL OBSERVATORY
PALISADES. NEW YORK
Technical Report
Contract AT (30- 1)1 114
Variations in the Isotopic Composition of
Common Lead and the History of the
Crust of the Earth
June, 1955
Digitized by the Internet Archive
in 2020 with funding from
Columbia University Libraries
https://archive.org/details/variationsinisotOObate
*
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■
Variations in the Isotopic Composition
of Common Lead and the History of
the Crust of the Earth
George L. Bate
J Laurence Kulp
June 1955
Submitted by George L. Bate in partial fulfillment of the
requirements for the degree of Doctor of Philosophy, in
the Faculty of Pure Science, Columbia University.
The research reported in this document has been made
possible through support and sponsorship extended by the
Research Division of the Atomic Energy Commission under
Contract AT (3C-1)-1114. It is published for technical
information only and does not represent recommendations
or conclusions of the sponsoring agency.
■
Table of Contents
Page
Abstract . v. . i
Introduction . 1
Acknowledgements . 4
Mineral Selection . 6
Experimental Procedure
Chemical Preparation of Lead Tetramethyl . 7
Contamination Effects . 7
Possible Fractionation . 8
Instrumentation of Mass Spectrometer . 9
Operating Characteristics of Mass Spectrometer .
Re solving Power . 15
Background and Noise Effects . 17
Drift in Ion Beam Intensity . 19
Hydride Formation . 19
Operational Procedure for Isotopic Analyses . 21
Calculation of Abundances from the Pb+ Spectrum . 21
Mercury Correction . 22
Drift Correction . 22
Scale Correction . 23
Hydride Correction . 23
Calculation of Abundances from
the Pb(CH3)^+ Spectrum . 25
Page
Re suits
Inter calibration Experiments . . . 28
Tabulation of Isotopic Analyses . 33
Age Relations for Various Earth Models . 60
Derivation of Step-Differentiation Model . 60
Comparison of Common Lead Isotopic
Data with the Step -Differentiation Model . 67
Least Squares Fit of Dated Samples to
Step- Differentiation Model . 68
Age Considerations . 68
Mathematical Analysis . 73
Model Embodying Continuous Differentiation
of the Earth's Crust . 81
Comparison of Lead Isotope Constants and
Age Derivatives with Previous Results . 91
Regional Analysis of Common Leads . 96
Joplin-Type Anomaly - The Mississippi Valley Leads. . . . 101
Geologic Setting . 103
Ivigtut Type Anomaly . 115
Additional Possible Factors Affecting
Isotopic Composition . • . . 115
Conclusions . 118
Bibliography
121
ABSTRACT
Isotopic analyses have been completed on 161 samples in a
reconnaissance of lead minerals from all the major continents, the
majority coming from North America. The analyses were made with
a 6-inch radius, 60° Nier-type, direction-focussing mass spectrometer
utilizing lead tetramethyl vapor for sample introduction. Intercalibra¬
tion analyses show that relative abundances of the three heavier isotopes,
Pb^6} Pb^^, Pb^8, obtained with the spectrometer agree to . 5%
with those reported by other investigators. Agreement on the lightest
Z 04
and least abundant isotope, Pb , is generally within 1%.
The majority of previous investigators have studied isotopic compo¬
sition of lead ores relative to their age and genesis on the basis of the
simplest possible model, herein referred to as the step-differentiation
model, which assumes broad uniformity of crustal conditions affecting
lead mineralization and neglects secondary effects. On the basis of this
model, isotopic compositions of the common leads reported in this work
are generally in agreement with their geologic age. Data for a few
dated samples have been fitted to the step -differentiation model by a
least squares analysis. The constants required for best fit are in good
agreement with those obtained by earlier workers, but incorporation of
meteoritic lead composition as primeval lead composition leads to an
age of the earth's crust which is considerably larger than those obtained
without meteoritic lead data.
This discrepancy has led to formulation of a model which permits
continuous differentiation of the earth's crust throughout geologic time
in an exponential manner. The constants introduced are evaluated
independently of lead ore data and these calculations show that the
maximum age of the earth is approximately 5. 3 billion years, this being
the time when terrestrial lead had the composition of meteoritic lead.
In like manner it is shown that the major portion of the differentiating
forces was expended in a time somewhat in excess of a billion years.
The isotopic composition of a number of leads is found to diverge
markedly from that predicted on the basis of the step -differentiation model,
and these anomalies are delineated together with their characteristics.
Special consideration is given to the Joplin-type anomaly which is charac¬
terized by a moderate excess of the radiogenic isotopes, and is found to be
prevalent throughout the several lead districts of the Mississippi Valley.
To account for this anomaly, a hypothesis is advanced which involves
inhomogeneous extraction of lead from original or contaminating sources.
In this process it is pictured that on the basis of the known tendency of
uranium and thorium to concentrate in interstitial rock material, their
lead end-products are more easily removed in solution than lead inside
mineral grains and thus give rise to leads with anomalously high radiogenic
isotope content. Calculations based on the excess Pb^^ and Pb^^ in a
number of the Mississippi Valley anomalous leads give an apparent age
of about 2 billion years for the excess lead in these samples.
li
Average isotopic compositions for the anomalous Mississippi
Valley leads and for other regions in the United States are tabulated.
Consideration of other possible factors affecting isotopic composition
leads to the conclusion that age, source, and mode of extraction are the
main factors controlling isotopic constitution of lead in common lead
minerals .
111
-
'
.
Introduction
The isotopic analyses of lead from twenty-five lead minerals reported by
12.
Nier and co-workers ’ in 1938-1941 showed that the isotopic composition depends
upon geologic origin. Nier postulated that the variations are due to the addition of
radiogenic lead (i.e. Pb^^, Pb^^> Pb^^ formed from radioactive decay of
238 235 232
U , U and Th respectively) to "uncontaminated lead" during geologic
time. He also suggested that this "uncontaminated lead" should be identified
with primeval lead, (German "Urblei") which may be loosely defined as the lead
present at the time of formation of the earth's crust. The remaining stable lead
204
isotope, Pb , is not known to be produced by any radioactive decay and all
204
Pb existing today is therefore regarded as primeval. Accumulation of nuclear
data and advances in nuclear theory since the Nier analyses have not revealed any
206 207 208
process in nature whereby appreciable amounts of Pb , Pb and Pb may
be formed (or destroyed), other than by the uranium and thorium decay schemes.
The current view on the geochemical occurrence of lead may briefly be
described as follows. Lead in nature is found either dispersed as rock lead or
concentrated as mineral lead. Since rocks also contain dispersed uranium and
thorium in varying concentrations, it is seen that the isotopic composition of rock
lead changes with geologic time due to the accretion of radiogenic lead from the decay
of uranium and thorium. Rock lead may be extracted and separated from the host
rock by various geochemical processes of differentiation and, depending on the
efficiency of separation from the uranium and thorium, three types of minerals
containing lead may be recognized: (1) common lead minerals, (2) uranium and
2
thorium minerals, and (3) mixed lead minerals.
If the separation of lead from a rock mass is essentially complete, common
lead minerals are formed. In this case the lead isotopic composition does not change
with time after the formation of the minerals and may reflect the isotopic com¬
position of the rock lead from which it was formed at the time of mineralization.
Common lead is most frequently found as galena, PbS. Uranium and thorium
minerals contain lead from radioactive decay of the parent elements. The
isotopic composition of the lead in these minerals changes with time and together
with chemical analyses for lead, uranium and/or thorium, may be used to
determine the age of the minerals by the several procedures of the lead-uranium
method of age determination. These minerals may contain some common lead
incorporated at the time of formation. Finally, if common lead and significant
radiogenic lead are both present it is designated a mixed lead mineral. In this
case the isotopic composition is independent of time although the 207/206 ratio
of the radiogenic component may give an indication of the time of formation.
Nier's common lead analyses formed the basis of a number of theoretical
3-11
papers , in which it was attempted to establish the following: (1) A satisfactory
model to account for lead ore formation from the rocks of the earth's crust; (2)
a value for the age of the earth's crust; (3) the isotopic composition of primeval
lead; and (4) a relation between the isotopic composition of mineral lead and the
age of the mineral. The last three items follow from the type of model proposed
11
in (1). McCrady has reviewed the papers prior to his publication.
More recently a new fund of common lead isotopic data has begun to be
, 12-15 _ 16-17 J 18
published by laboratories in Canada , Germany and the U. S.S.R.
These data, together with Nier's original results have received further analytical
3
19, 20 21
treatment by Damon and have been summarized by Houtermans • The various
workers in the field have consistently cited the need for more lead isotopic abundance
data.
The present work was undertaken with the purpose of (1 y conducting a reconnais¬
sance of common lead minerals of world -wide distribution to add to the growing fund of
lead isotopic abundance data, and (2) to catalog in more detail the variations in
isotopic composition of common lead in the United States, The data obtained pro¬
vide the basis for a number of theoretical conclusions: (1) New limits on the
possible variations in isotopic composition in various geologic settings can be
defined. (2) This makes it possible to identify anomalous leads with greater
certainty. (3) A revised model of crustal differentiation can be proposed. (4) The
age of the earth's crust can be reassessed. (5) The relative abundances of uranium
and thorium to lead in the earth's crust can be reevaluated. (6) It is possible to
limit the speculation on the mechanism and origin of lead-ore formation. In
summary, the acquisition of new common lead isotopic data permits further study
of the history of the earth's crust, both in the broader aspects of crustal formation
and composition, and in the local aspects of mineral formation throughout geologic
time at various differentiating foci,
The authors wish to express their appreciation for the helpfulness and interest
of a number of geologists in making this research possible. Several members of
the Geology Department of Columbia University have contributed materially to the
success of the work. Professor C. H. Behre, Jr. encouraged the undertaking of
the research program and made accessible the Economic Geology Collection for
the selection of lead ore specimens, and provided valuable information on the origin
of these samples. Through the courtesy of Professors P„ F. Kerr and R. J. Holmes,
the Systematic Mineralogical Collection was made available for sample selection
and information on pertinent mineralogy was generously provided. Professor G. M.
Kay contributed helpful advice on stratigraphic problems connected with the dating
of mineral specimens. Through the office of Professor A. Poldervaart a galena
sample from South Africa was supplied, and we are also indebted to Dr . Poldervaart
for assistance in communication with the various Geological Survey Offices in
southern Africa. Through the kindness of Professor B. H. Mason and D. M. Seaman,
several samples were obtained from the American Museum of Natural History. An
additional note of appreciation is due Dr. Mason for calling our attention to the
Vesuvius sample recently acquired by the Museum.
The authors are especially indebted to the Offices of the Geological Survey of
South Africa and of Southern Rhodesia for their excellent cooperation in providing
a suite of common lead minerals from various pre-Cambrian strata in southern
Africa. Dr. L. T. Nel, Director and Dr. B. Wasserstein of the Geological Survey
of South Africa provided eight samples together with a description of their geological
environment, from the Union of South Africa. A similar set of samples from
5
Southern Rhodesia with descriptions was supplied by Dr. R. M. Tyndale -Biscoe,
Acting Director, assisted by Dr. A. M. Macgregor, of the Geological Survey of
Southern Rhodesia.
The original mass spectrometer tube was designed and constructed by H. R.
Owen. W. R. Eckelmann worked out the initial chemistry of lead tetramethyl
preparation. Technical assistance on routine operations was necessarily extensive.
J. Gaetjen, R. Nuckolls, J. Miller and M. Trautman assisted with tetramethyl
preparation; D. Miller, W. Knox and J. Hoover helped with routine spectrometer
operation; M. Feely, L. Tryon, J. Averill and A. Toleno assisted with the
abundance computations. The valued assistance of our instrument makers, W.
Tamminga and F. Gwinner, is also acknowledged with appreciation. W. F. Kelly
assisted with bibliographic research on the geologic origin of various lead deposits.
Financial support was provided by the Atomic Energy Commission under contract
AT(30-1)1114. The senior author acknowledges with gratitude the grant of a pre-
doctoral fellowship from the National Science Foundation, under tenure of which this
research was initiated.
6
Mineral Selection
The choice of comm n lead minerals was restricted largely to those available
in the various mine r alogical collections so generously placed at the disposal of
this laboratory. The samples were selected with as widespread distribution both
in geographic location and geologic setting and age, as possible. Several suites of
samples were chosen with a common geologic environment but with different mineral
form, different mineral associations, etc. , in order to search for possible effects
on isotopic composition. In one case, two samples were taken from opposite ends
of a large galena crystal in order to check possible isotopic fractionation with crystal
growth. In some cases more than one sample was taken from a given locality
with the purpose of checking variations in random samples.
It will be noted (see Table II) that for some of the localities selected, common
lead analyses have previously been reported in the literature. The Lamont data
for these localities are included here however, not only to permit comparison
with the earlier analyses, but also to present the whole body of data accumulated
with the use of one mass spectrometer at this laboratory. By way of summary
for the 161 samples shown, a total of 121 localities are represented, 100 of which
are new localities, without previously published common lead anaylses.
Although the mineralogical collections were invaluable for the acquisition of
samples, the value of some of the samples is diminished because of the lack of full
description of the geographic and geologic source. A typical difficulty encountered
is that some samples were originally collected from small mines whose operation
ceased many years ago; consequently little or no further information can be obtained
at the present time. In any event, the table contains all the pertinent information
as to geographic origin and mineral association obtainable with each specimen.
7
Experimental Procedure
Chemical Preparation of Lead Tetramethyl
In order to introduce the lead into the mass spectrometer in gaseous form it
was necessary to synthesize lead tetramethyl PbfCH^)^ from the mineral lead
22
samples. The general technique has been described in the literature and
consists briefly of: preparation of pure lead chloride from the lead mineral;
Grignard reaction with lead chloride; hydrolysis of excess Grignard agent;
separation of ether solution of tetramethyl from water solution; separation of
tetramethyl from ether by fractional distillation, completed by evaporation of
excess ether under reduced pressure, until the vapor pressure corresponding to
that for lead tetramethyl was observed on a mercury manometer. With an initial
charge of about .3 gram lead chloride, the final yield of tetramethyl was of the
order of a few hundredths milliliter by volume, sufficient for several runs of the
spectrometer .
Contamination Effects
The possibility of appreciable lead contamination from the chemical reagents
employed was ruled out on the basis of the following considerations. Only reagents
of the highest purity commercially available were used and the possible lead
content specified was very small compared to the amount of lead in the sample.
Moreover, any lead present in the reagents would have been, most likely, common
lead, and since the isotopic composition of common leads varies over small limits
only, the effect on the isotopic composition of the sample would have been
negligible. This conclusion was verified by two pieces of experimental evidence.
(1) An intercalibration sample was received in the form of metallic lead, and the
typical chemical procedure in its entirety was used to prepare the lead tetramethyl
8
required for the analysis. The isotopic composition obtained was very close to
that reported by other investigators for the identical sample (see Table I). (Z) An
even more conclusive proof was demonstrated in the following manner. A lead
iodide salt was divided into two portions, one of which was converted into lead
chloride for the Grignard reaction. Since the Grignard reaction will also take
place with other halides, the remaining iodide portion was utilized directly for
the Grignard reaction. The lead isotopic compositions of the two tetramethyls
thus prepared were identical within limits of experimental error, and it was
therefore concluded that contamination from inorganic reagents, the most likely
source of contaminant, was negligible.
It was found that heavy organic residues were present in the tetramethyl
• I
sample, which could contribute to ion signals in both the Pb spectrum and in the
trimethyl spectrum. These impurities exhibited low vapor pressures relative to
Pb(CH^)^ and were a source of trouble only if the sample container was heated.
It was found that initially all of the Pb(CH^)^ could be transferred to the manifold
by putting liquid air on a finger in the manifold while the sample container remained
at room temperature. This process did not introduce any appreciable contaminants
into the leak of the mass spectrometer.
Possible Fractionation
Further tests were conducted to detect any fractionation effects in the chemical
procedure. It may be noted that in the last two steps of ether removal by fractional
distillation and by evaporation, the effect of isotopic fractionation would be such as
to favor removal of the lighter isotopes and thereby increase the percentage com¬
position of the heavier isotopes in the residual sample. For the typical sample,
9
the fractional distillation reduced the volume of the ether solution by a factor of
about 4 and the final evaporation involved a volume reduction by a factor of about
100. Although the predicted fractionation at the boiling temperature of the mixture
204 206 207 208
based on the mass difference of the Pb (CH3)4, Pb (CH3)4> Pb <CH3)4,pb (Ch3)4
molecules, is negligibly small, two experimental tests were resorted to for the
final proof. These tests simply consisted of repeating the fractionation and
evaporation process two times, one process at a time, after adding a volume of
ether equal to that just removed. Any effect originally present would have been
multiplied by about a factor of 3, but although the tests were repeated several
times on two different samples, no change from the original isotopic composition
could be detected.
It is believed therefore, that errors in the data due to contamination or
isotopic fractionation in the chemical preparation process are well within the
experimental error reported.
Instrumentation of Mass Spectrometer
The mass spectrometer employed for the isotopic analyses was a direction¬
focussing 60° sector type instrument of glass-metal construction with 6" radius,
23
previously made at this laboratory after a design originally reported by Nier
Following several modifications a mass resolution of better than 1 part in 220 was
obtained, together with other characteristics suitable for work with the Pb+ spectrum.
A later re-alignment of the entrance and e:>y.t slits gave a mass resolution of nearly
1 part in 300, which permitted satisfactory operation in the range of the trimethyl
spectrum.
10
The most important modification consisted of the utilization of a new source,
24
designed essentially after that described by Palmer and Aitken (Figure 1). The
exit slit of the source was made .075 mm wide, and the entrance slit at the collector
was made .3 mm wide in order to give maximum signal with optimum resolution.
With these slit configurations the typical ion current at mass 208 was of the order
of 10 ampere.
204
In order to avoid Hg at mass number 204, an oil diffusion pump was
initially used to provide high vacuum in the tube. However, on prolonged use,
increasingly large backgrounds of organic origin were encountered in the mass
range of the lead spectrum, particularly at mass number 207. This background
was essentially eliminated on replacement of the oil diffusion pump with a
mercury diffusion pump. The 3 -stage mercury pump also lowered the ultimate
vacuum of the system to an indicated pressure (Research Corp. ionization gauge)
- 8
of 5 x 10 mm Hg., as well as providing a considerable improvement in the
pumping speed of the system. The fore vacuum was maintained by a mechanical
pump of 58 1pm free air capacity and rated with an ultimate vacuum of .1 micron.
A commercial high voltage supply (Beva Model 301) proved very satisfactory
for the high voltage required for ion acceleration. The accompanying voltage
divider loop was designed for our particular source requirements and is shown
schematically in Figure 2. The electromagnet and magnet supply were also
commercial items.
The emission regulator was slightly modified from a design reported in
25
the literature . The schematic circuit is shown in Figure 3. The time constant
11
Filament
Stainless steel source plates.
Quartz glass spacers and
insulators.
Source slit .65 mm.
Draw out,
plate separation .35 mm.
Focus, plate separation .35mm.
Aligning Slit .15 mm.
Centering, plate separation .35 mm.
Exit slit . 075 mm.
SOURCE
FOR MASS
ASSEMBLY
SPECTROMETER
Figure 1. Source Assembly for Mass Spectrometer
Figure 2. Schematic of High Voltage Divider Circuit for
Mass Spectrometer Source
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of the control circuit was highly sensitive to the value of condenser Cj and
values larger than .01 jxf were found to give rise to regenerative conditions.
A commercial vibrating reed electrometer (Applied Physics Corp. Model
30) gave satisfactory amplification of the ion currents received at the collector.
A voltage signal was developed in the usual manner by passing the ion current
through a grid resistor of large resistance. The optimum value of 10^ ohms
for the grid resistor was obtained by compromising the requirement of maximum
signal with that of minimum noise for the greatest amplification used. The
resultant time constant was larger than desired and necessitated a relatively
slow scanning rate in order to allow the full signal to be developed at the peak
heights .
With later improvement of the resolution and sensitivity which permitted
use of the trimethyl spectrum, a grid resistor of 10 ^ ohms was found to be
very satisfactory. This change substantially reduced the input time constant
of the detecting system and permitted more rapid scanning.
The output of the vibrating reed electrometer was fed to a pen and ink
recorder through a decade resistance box which served as a voltage multiplier.
The gain control on the electrometer, together with the following voltage
multiplier bridge permitted a complete range of amplification of ion current
signals. The linearity of amplification of the combined system was checked
by applying known signals from a standard potentiometer to the reed input.
The sample introduction system was made as simple as possible. In order
to avoid contamination (from mercury or organic vapors) from diffusion pump
vapors, the vacuum in the sample manifold was supplied solely by a mechanical
pump followed by a liquid air trap. With an ultimate vacuum rating of . 1 micron
15
Hg, the mechanical pump gave good pumping characteristics. It was found
that tetramethyl vapor was readily absorbed on all types of stopcock grease,
and it was therefore necessary to use a metal manifold with all-metal needle
valve s .
The sample pressure was reduced by admitting the gas into the spectro¬
meter through a viscous leak. The leak was made by drawing out glass
capillary tubing, giving a final capillary of some 30" in length with an average
diameter of about 4 mils. A specially constructed gas inlet system for transfer
of the gas from the low pressure side of the leak into the ion source proper is shown
in Figure 4. This system provided for a highly efficient transfer of the gas,
with the result that typical analyses were made at indicated tube pressure of
-7
1 - 4 x 10 mm Hg.
Operating Characteristics of Mass Spectrometer
Resolving Power
A useful and perhaps more definitive index of resolving power than the
, , 17
customary mass resolution, is the quantity Q defined by Geiss , e.g., as
the ratio of the ion current minimum between the peaks at mass numbers 207
and 208, to the maximum ion current at mass number 208. The optimum value
obtained for our spectrometer was Q 05%, while for the average analysis
the value of Q might be as high as . 3%. However, it was shown that for even
higher values of Q the effect on the peak heights and therefore on the apparent
isotipic composition varied only in a secondary manner with Q.
Extensive tests were made to determine the factors affecting Q, inasmuch as
the resolving power occasionally became very poor, with no known change of
Figure 4. System for Transfer of Sample Gas to Ionization Chamber
16
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17
the control parameters. No dispersion due to pressure effect alone could be
established and none would be expected since the indicated tube pressure
, -7
during analyses never exceeded 5 x 10 mm Hg. Variation of the position
of the aligning magnet, of the source plate potentials, and of the electron
accelerating potential affected primarily the intensity of the ion beam, and
had little if any effect on the resolving power. It was observed however, that
the resolution invariably decreased when considerable impurity (primarily
ether) was present in the sample and moreover the apparent dispersion increased
during an analysis. It was finally concluded that the primary cause of loss of
resolution was the accumulation of surface charge on the walls of the tube. The
-11
fact that small ion currents (about 10 ampere maximum) were employed,
made the instrument especially sensitive to surface charge accumulation.
Preventive measures to avoid surface charge effects consisted of maintenance
of clean metallic surface conditions within the tube, and of regular heating of
the tube between runs.
In general, the resolving power of the instrument is considered more than
adequate for the lead isotopic abundance reconnaissance undertaken in this
work. Even for work on a regional basis the inherent resolution is sufficient,
unless differentiation of isotopic compositions to better than .3% is required.
Background and Noise Effects
With the introduction of a mercury pump the background mass spectrum
was reduced to a negligible level. After extended use a background common lead
spectrum was consistently present, but since the 208 peak height was of the
order of 1 mv, the background effect was disregarded in comparison to actual
18
sample signal, for which in a typical analysis the 208 peak height lay in the
range of . 5 - 1 volt. A substantial background signal was rarely observed
in the trimethyl spectrum. The tube was baked for about 15 minutes between
runs primarily to dissipate surface charge accumulated within the tube, and
this procedure also had the beneficial effect of essentially eliminating memory
effect from the preceding sample. The pumping speed of the vacuum system
was such that on sample removal, peak heights were decreased by a factor
of several hundred within a few minutes' time.
The use of a mercury diffusion pump necessarily introduced a background
mercury spectrum which, under conditions of sustained baking, could not be
204
entirely eliminated. However, since Hg constituted about only 1% of the
204
signal at mass number 204, it is evident that errors in the Hg correction
204
can contribute only errors of the second order to the Pb abundance.
The maintenance of a low noise level in the amplifying system depended
in a critical manner upon proper shielding of the ion collector. With optimum
shielding the noise level was of the order of .05 mv, which is quite negligible for
i 204
the heavier isotopes and is not serious for the smaller Pb isotope, the
signal for which rarely was less than 10 mv. The usual stability problem in
a high-gain d.c. amplifier was not encountered with the vibrating reed
electrometer, due to the reed method of changing the d.c. signal into an
a.c. signal. The short term drift of the particular vibrating reed electro¬
meter used was stipulated not to exceed .004 mv/sec, well within the required
accuracy of analysis.
19
Drift in Ion Beam Intensity
With the higher value of input grid resistor previously noted, the time
constant of the amplifying system was about 1 sec. With the relatively slow
scanning rate required to permit full development of signals, the time required
to scan through the lead spectrum from mass number 202 was about six minutes.
Coupled with a drift rate in ion current of about . 2% per minute, this factor was
probably the major source of experimental uncertainty. The magnitude of the
effect was substantially reduced, however, ny applying a drift correction based
on the assumption of a linear variation, to the recorded peak heights. This
assumption was justified on the basis of the following two considerations. First,
direct observation of drift by "sitting" on a peak showed that the drift rate was
essentially linear. In the second place, the isotopic composition calculated
with drift correction was identical to within .1% to that obtained without drift
correction, the major difference being that the deviations were substantially
reduced. Since the spectra were scanned alternately up-mass and down-mass,
a composition calculated without drift correction would be expected to cancel
the drift effect if the drift rate were linearly uniform. The fact that identical
composition was obtained with both methods of calculation was taken as an
indirect verification of linearly uniform drift rate.
Hydride Formation
A variable of particular importance in using the Pb spectrum from Pb(CH^)^
vapor is the formation of PbH^ . The efficiency of hydride formation is pressure
and temperature dependent. However these variables are not known to change
appreciably during the course of an analysis, and the hydride efficiency was in
20
fact never observed to change significantly during a run and was remarkably
constant from day to day for long periods of time. The hydride efficiency is
calculated from the ratio of the peak height at mass number 209, due to the
208 +
hydride Pb H , to the peak height at mass number 208.
The hydride factor was found to be very sensitive to the electron accelerating
voltage, which was variable over a range of about 90 volts. The isotopic com¬
position of a sample was shown to be independent of the electron accelerating
voltage, E , and hence independent of the hydride efficiency. It was found that
the ion current increased with electron accelerating voltage to a maximum at
about 40 volts, and then decreased on further increase of electron accelerating
voltage. Higher values of the electron accelerating voltage were found to give
rise to unstable source conditions and most of the analyses were therefore made
with Eg = 40 volts. For this value of Ee, the efficiency of hydride formation
was approximately 10%.
The operating performance of the spectrometer may finally be evaluated on
the basis of the reproducibility of isotopic composition of a given sample. A
reference standard sample of tetramethyl was analyzed nearly 40 times during
the course of sample analyses, involving a time span of approximately one year.
The average deviation of an analysis from the mean was about . 2% for the
204
heaviest isotopes and nearly . 5% for Pb . These variations were usually
within the deviation of each individual analysis. The greatest deviation observed
was about .4% for the heaviest isotopes and 2% for Pb^^.
21
Operational Procedure for Isotopic Analyses
The sample schedule was arranged so that no sample was analyzed twice in
the same day, at the same time providing for a change in sample order on
repeat analyses. With but few exceptions, all samples were analyzed at least
twice. Two analyses usually gave results within the average deviations of each
other and a third analysis was made if this condition was not met. Most of the
analyses consisted of 10 single-peaked spectra or the equivalent.
The purity and amount of sample were initially checked by the nature of the
spectrum obtained with a given sample manifold pressure and resulting tube
pressure. Any sample purification further required was accomplished by
pumping off repeated portions of the ether-rich vapor. For the typical analysis
a sample pressure of about . 5 mm Hg was required.
Allowing for tube bake -out between runs, the usual routine permitted 5
analyses during a 10 hour period. The reference tetremethyl standard was
analyzed at various intervals to detect possible changes in performance of the
instrument. For several of the Nier samples the reference tetramethyl was
run before and after each analysis.
In general, the large number of analyses per unit time is the main advantage
of the tetramethyl method. Without such a facility the number of samples herein
reported would not have been possible.
Calculation of Abundances from the Pb^ Spectrum
The sequence of computation for calculating the isotopic abundance from an
+ 204
analysis of the Pb spectrum consists of: (1) correction of 204 peak for Hg ;
(2) correction for drift in ion current intensity; (3) correction for resistance of
secondary multiplier bridge coupled with (4) reduction to common scale on the
22
basis of amplification factors used; (5) reduction to percentage composition;
and finally (6) hydride correction.
Mercury Correction
The mercury correction was made in the usual manner by computing the
^ Q ^ ^ Q ^
amount of Hg from the amount of Hg at mass number 202, using the
204 202 . 204 202
known ratio of Hg / Hg . The measured ratio of Hg /Hg from back¬
ground spectra agreed with the value cited in the literature within the experi¬
mental error; however, the accepted value was used in the calculations due to
the large uncertainty in the measured ratio, resulting from the small signals
204
invloved. As noted previously, the amount of Hg in the typical analysis was
about 1% of the total 204 peak; hence any reasonable uncertainty in the
204 202 204
Hg /Hg ratio would have a very small effect on the Pb abundance.
It was observed, however, that for some extreme cases in initial test analyses
204 204
for which Hg comprised about half the signal at mass 204, the Pb abundance
204
was experimentally identical to that later obtained with Hg down to the one
per cent level. This was taken as evidence that the ratio used for Hg^^/Hg^^
was correct.
Drift Correction
Occasionally the change in ion current intensity during an analysis was so
small that the drift correction was not necessary; but for most analyses it was
necessary to apply the drift correction in order to obtain a true picture of the
deviations. Since the 208 peak was the largest, the drift correction was applied
so that all other peak heights were computed to give their true values at the time
the 208 peak was recorded. The correction was computed by pairing spectra scanned
23
up-mass and down-piass and obtaining for each set an average drift rate from
the percentage changes in peak height of the three heavier isotopes. The remainder
of the calculation follows in a straightforward manner and, as noted before, is
perfectly valid providing the drift rate is uniformly linear.
Scale Correction
When adjusting for the scale of amplification used, an additional small
correction was made for the resistance of the voltage multiplier bridge follow¬
ing the vibrating reed electrometer. The resistance employed on the voltage
multiplier varied from 10 to 90 ohms (to supply signal to a 10 mv recorder from
maximum 1 ma reed current), which was not negligible compared to the electro¬
meter output loop resistance of 2000 ohms. The correction follows directly
from an elementary application of Ohm's law.
Hydride Correction
The true abundance of the isotopes is calculated from the peak heights observed
on the recorder chart in the following manner. Let 204', 206', 207', 208' and
204
209' represent the observed peak heights of these isotopes (2041 excludes Hg )
and let 204, 206, 207, and 208 represent the corresponding true abundances.
Both sets of numbers express percentage composition. The true hydride factor
may then be written as:
C = 2097208 = PbZ08H+/Pb208+.
From the nature of the hydride formation, the following equations can be
written:
204' = 204 - C(204) = (1-C) 204
206' = 206 - C(206) = (1-C) 206
(1)
(2)
24
207' a 207 - C(207) + C(206) = (1-C) 207 + C(206)
208' a 208 - C(208) + C(207) a (1-C) 208 + C(207)
C
Now writing k a ^ji q} » foregoing equations become:
204 = ( 1 + k) 204'
206 a (1 + k) 206'
207 = (1 + k) 207' - k (206)
208 a (1 + k) 208' - k (207)
(3)
(4)
(5)
(6)
(7)
(8)
Equations (6), (7), and (8) are actually three non-linear equations in the
unknowns 206, 207, and 208, for which the exact analytical solution becomes
somewhat cumbersome. This difficulty may be avoided and the roots may be
obtained with the desired accuracy by using repeated approximations. For the
first approximation k' =s 209'/208', and corresponding values of 206', 207', and
208' are calculated. The next approximation of k is k" = 209'/(208'-209') and
corresponding values of 206" and 207" and 208" are computed. This is then
followed with k"' = 209' /(208" -209'), etc., until the required precision is
obtained. Usually the closure is so rapid that two approximations suffice.
For a given analysis, 204', 206', .207', 208', and 209' are actually the
averages of percentage compositions of the individual scans comprising the
analysis. For each average ion abundance an average deviation is computed.
The average deviations of the true composition will have added uncertainty due to
the error in the 209' peak. The effect of the hydride error was calculated for
each analysis, but invariably the contribution to the error in the true composition
was found to be small, usually negligible. The relative error in 209' never
exceeded 1% and the resulting uncertainty contributed to the true abundances of
the lead isotopes rarely approached .1%.
25
It is to be noted that the foregoing hydride correction assumes that the
208
hydride efficiency obtained for Pb applies to the remaining lead isotopes.
A possible systematic effect violating this assumption would consist of a mass
discrimination in hydride formation. If such an effect did exist, the hydride
r . r t-,,204 ?08
factor for Pb would differ to the greatest extent from that obtained by Pb
204
However, even for Pb , the greatest possible effect on k, assuming a functional
dependence as the square root of the ratio of the masses, would not exceed 1%.
A systematic error in the hydride factor of this order of magnitude would
introduce an uncertainty in the true abundances well within the experimental
error reported.
Calculation of Abundances from the Pb(CH^)^+ Spectrum
In the trimethyl mass region (mass numbers 248 through 254) there is no
interference from mercury. The drift and scale corrections are made in an
identical manner to that described under the calculation of abundances from the
Pb^ spectrum. The hydride effect is present but to a lesser extent than in the case
I -j-
of the PbT spectrum. Additional corrections must be made in the PbfCH^)^
13 12
spectrum for the C /C effect and for the loss of a hydrogen atom.
The analytical expressions for the Pb(CH^)^+ spectrum may be developed
as follows. Let 249', 251’, 252', 253', and 254' represent the observed signals
at these mass numbers. Also, designate by 249, 251, 2 52, and 253 the true
204 206 207 " 208
abundances of Pb , Pb , Pb , and Pb , respectively, appearing at the
13 12
indicated mass numbers in the trimethyl spectrum. The C /C ratio and hydride
formation have the same effect of increasing the observed signal at mass number
(m + 1), at the expense of the signal at mass number m. Let p therefore represent
26
the fraction of the true signal at mass number m appearing at mass number
13
(m + 1) due to the combined effects of hydride formation and C appearance.
Similarly, let q represent the fraction of the true signal at mass number
m lost to mass number (m - 1) due to the loss of one hydrogen atom. Neglect¬
ing second order effects, the observed spectrum may be analytically expressed
as follows:
249' = 249 - p(249) - q(249 = 249(1 - p - q) (9)
251' = 251 - p(251) - q(251) + q(252) = 251(1 - p - q) + q(252) (10)
252' = 252 - p(2 52) - q(252) + p(251) + q(253) = 252(1 - p - q) + p(251) + q(253) (11)
253' = 253 - p(2 53) - q(253) + p(252) = 253(1 - p - q) + p(252) (12)
254' = p(2 53)
r
Writing r = p + q and s = ^ - — , equations (9) through (12) may be implicitly
solved for 249, 251, 252, 253:
249 = (1 + s)249' (13)
251 = (1 + s)251' - q(l + s)252 (14)
252 = (1 + s)252' - p(l + s)251 - q(l + s)253 (15)
253 =e (1 + s)253 - p(l + s)252 (16)
As with the Pb+ spectrum, equations (13) through (16) may be solved by repeated
approximations, q was found to have a value consistently in the neighborhood of
1%. Small variations in this value would have a negligible effect on the final
abundances. The value of p was fairly constant at 3.2%. If the C /C ratio
is taken as .011, then the trimethyl hydride effect amounted to about 2.1%. This
value is considerably larger than that of 0. 33% reported by Dibeler and Mohler2^
and that of .08% reported by Collins, Russell and Farquhar . The different
values 0. 33%, .08% and 2.1% are due presumably to differences in temperatures
27
of the sources, in geometric configurations of the electron beam, and in
conditions of secondary emission.
The corrections in the trimethyl spectrum are therefore about one -third that
in the Pb+ spectrum. This is particularly important for the analysis of radio¬
genic lead where the correction factors from preceding and following common
lead analyses must be assumed to be constant.
28
Re suits
Intercalibration Experiments
In the absence of a lead standard of known absolute isotopic composition,
the only possible recourse to check possible systematic discrimination by a
given mass spectrometer is to make comparison analyses of samples analyzed
on other spectrometers. Unfortunately, at the time of research herein reported,
no systematic program of comparison of lead samples at different laboratories
was yet in effect, with the exception of the circulation of a reference lead
sample by the United States Geological Survey. However, through the excellent
cooperation of interested investigators, a number of samples were obtained which
provide the basis for a correlation of the performance of our instrument with
that of instruments at other laboratories.
The largest suite of samples for comparison purposes was provided by
Dr. J. P. Marble jn the form of a number of the identical lead salts used by
1 2
Nier in his work ’ previously referred to. The United States Geological Survey
has recently circulated a "standard" lead sample for intercalibration purposes,
and through the courtesy of Dr. L. R..Stieff, a portion of the U. S. G. S. "standard"
was provided for this work. This identical sample has also been analyzed at
Toronto, Canada, and at Harwell, England. Finally, two more samples were
obtained which had been analyzed at Toronto and Oak Ridge.
The comparison of analyses of identical samples is displayed in Table I. All
of the Lamont analyses shown are based on the Pb+ spectrum, but later analyses
of our reference standard in the trimethyl region gave results identical to those
obtained on the basis of the Pb^ spectrum. The comparison is even more significant
in view of the different methods used for sample introduction. The lead was
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volatized from solid lead salts in the instruments used by Nier, Oak Ridge,
and Harwell, while lead tetramethyl vapor was employed at Toronto and Lamont.
The Toronto results also include analyses based on the lead trimethyl spectrum, in
addition to the Pb"^ spectrum. It is significant that in spite of the considerable
differences in chemistry, in method of ion formation, etc. , the results are
comparable to within a fraction of a per cent for the heavier isotopes, and to
the order of a per cent for Pb^^. The greater divergence of values for Pb^^
is to be expected from the relatively small signals obtained at mass number 204.
The results from the various laboratories are of further interest in that
different geometry was used for beam collimation and focussing. The Nier
spectrometer and the Toronto spectrometer were both 180° instruments while
the Lamont, Harwell and Oak Ridge spectrometers are 60° instruments. In
all cases magnetic scanning was used.
The Lamont analyses are averages of at least three runs in most cases.
The Wallace, Idaho, cerussite was analyzed about a dozen times, for reasons
enumerated below. The Pb^^ composition is shown with parentheses about
204
the fourth significant figure in order to emphasize that Pb does not have
associated with it the same relative precision as in the case of the heavier
isotopes .
A very close comparison of the Lamont analyses with the Nier analyses is
not possible since Nier's numbers are stated to have a probable error of about
. 5%. It is observed that with the exception of Nier's sample No. 10 (Lamont
No. 23), the compositions for the heavier isotopes generally agree within . 5%,
204
while the divergence for Pb may approach 2%, but more usually about 1%.
204
A greater spread is to be expected for the Pb values, but it nevertheless
32
seems evident (see especially the seventh column in Table I) that relative to
204
Nier's values, Pb is suppressed in the Lamont analyses. Such an argument
204
based on comparison of Pb compositions alone would not be conclusive;
however, the same trend is definitely reflected in the heavier isotopes (note
especially the last column in Table I). Although the differences invloved lie
within the experimental uncertainty, the statistical weight of the numbers shows
a trend toward a lower abundance of the lighter isotopes in the Lamont analyses
as compared with those of Nier.
The distinct discrepancy between the analyses on the cerussite from Wallace,
Id. (Nier No. 10) has no explanation. The sample was repeatedly analyzed under
varying conditions, but the isotopic composition consistently differed as shown
from that reported by Nier. It is suggested that the sample had in some manner
become contaminated.
A comparison with more recent instrumentation is provided by the remaining
analyses shown in Table I. For the U . S . G. S ." standard" the Toronto anaylsis is
an average of five runs, four of which utilized the trimethyl spectrum and the
fifth the Pb spectrum . The Harwell analysis is an average of seven runs -
three based on the PbCl+ spectrum, two on the Pbl+ spectrum and two on the
Pb+spectrum. Two analyses are shown for the Lamont measurements, and
although the operating conditions were not highly satisfactory, circumstances
prohibited further analyses prior to this publication.
In general, the analyses on the U.S.G.S. standard agree to about .3% for
the heavier isotopes and the probable error in values for Pb^4 is less than 1%.
For the remaining two samples the Lamont analyses are roughly intermediate
between those reported by Oak Ridge and Toronto. The Goldfields No. 1 sample
33
has an anomalous composition and the discrepancies between the analyses are
considerable. However, this sample was known to contain a small amount of
uranium and the spread in composition reported may merely reflect inhomo¬
geneity of samples. The Goldfields No. 2 is a more typical common lead and
for this case the Lamont and Toronto values are in good agreement.
More data and greater precision are necessary for conclusive comparisons,
but at this point there is just a suggestion that instruments utilizing volatilization
of lead from the solid state give analyses tending to suppress the heavier isotopes,
compared with analyses obtained with tetramethyl vapor. The internal precision
claimed for the Lamont data is of the order of .2% for the heavier isotopes and
. 5% for Pb . On the basis of the foregoing comparisons, the Lamont analyses
are comparable to those of the laboratories cited within . 5% for Pb^^, Pb^^,
and Pb^^ and to within 1% for Pb^^.
Tabulation of Isotopic Analyses
The isotopic abundance data for the samples analyzed are tabulated in Table
II according to geographic distribution. Of the 161 analyses shown, the majority
are for samples from the North American continent. Unless otherwise noted,
the mineral samples were obtained from the Economic Geology Collection and
from the Systematic Mineralogical Collection, both of the Department of Geology
of Columbia University. Most of the analyses were made with the Pb+ spectrum.
Those based on the trimethyl spectrum are denoted with an asterisk (*).
Although the experimental uncertainties for the various analyses do not vary
greatly, they are shown as average deviations for each analysis in order to show
to some extent the analyses with which greater precision can be associated. In
Isotopic Abundances of Common Lead
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1.000 18.57 15.67 38.83
126 Derbyshire Galena 1.35(0)±.004 25.07±.03 21.16±.04 52.42±.05 .8440 2.091
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1.000 18.80 15.67 38.99
133 Zinc Mines, Laurion Galena 1.34(3)±.005 25.25±.04 21.05±.02 52.36±.06 .8337 2.074
Table II, Continued :n
Mineral
Locality _ Description _ 204 _ 206 _ _ 207 _ 208 _ 207/206 208/206
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^ Sample provided by United States Atomic Energy Commission, Raw Materials Division
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54
some cases, the uncertainty is somewhat larger than that indicated, owing to
the fact that further analysis was necessary but prohibited because of sample
loss. For most data, at least two runs were available and these were averaged
together, weighting each run according to the number of scans comprising it
and weighting each isotope inversely to the square root of the average deviation
associated with it. Such a weighting procedure admittedly suffers statistically
because of the small number of runs per sample, but is is believed to serve
at least as a good first approximation.
As noted previously, not all of the localities represented are "new" in that
isotopic analyses have not previously been reported for the given source. For
those sources from which samples have already been analyzed, the previous
analyses, where available, have also been given for comparison purposes.
Analyses by other investigators on identical specimens are included only in
Table I, and all the ’’outside" analyses reported in Table II are on non-identical
samples from the same locality. It is interesting to note that for three such
samples in particular, namely nos. 17 (Sudbury, Ont. ), 19 (Ivigtut, Greenland),
and 130 (Langban, Sweden), the agreement with the Toronto and Nier analyses is
better than that generally obtained for that between analyses of identical samples
in Table I.
For each analysis the isotopic composition is reported in two ways - with
204
Pb = 1.000 in the first line, and with the normal percentage composition in
the second line. The corresponding deviations are not shown for the first manner
of presentation, but may be calculated if desired from the deviations given with
the percentage composition. It is evident that such deviations will be larger
than the latter because of the combination with the large uncertainty in Pb^®^.
55
For further comparison of the Lamont analyses, the ratios Pb2^/Pb2^8
and PbZ08/Pb20' k are shown in the last two columns as arbitrary indices.
These quantities, it is to be noted, are not affected by the large uncertainty
in Pb204.
The classification of the lead minerals as common lead (i.e., containing no
radioactive elements) was loosely made on a mineralogical basis; it was not
considered necessary to actually monitor any of the samples for possible radio¬
activity. It was known however, that the suite of Goldfields samples (Nos. 9-13)
contained small amounts of uranium. These samples are not common leads,
but rather mixed leads, but are included in the table to illustrate the possible
variations in the isotopic composition of lead minerals in the region where they
are formed from an environment containing high concentrations of radiogenic
lead. Samples 9, 10, and 13 clearly show the presence of radiogenic lead,
while sample 12 has an anomalous common lead composition and constitutes an
interesting transition into the common lead field.
An arbitrary but useful display of the variations in isotopic composition of
lead may be had by utilization of a triangular diagram as shown in Figure 5.
Here the percentage compositions (recalculated to 100%) of the three heaviest
isotopes, Pb^k, pb2^, Pb^^ t are plotted in the usual triangular mode
(there are actually only two independent variables). The field in Figure 5
is arbitrarily bounded by the vertex points of 32%, 28% and 60% of Pb2^8, Pb^ ^
208
and Pb respectively, and this field will be referred to as the (normal) common
lead field. The position of the common lead field in the total field is shown in
Figure 6, together with a plot of some samples whose composition falls outside
the common lead field. The chief advantages of the triangular mode of repre-
Figure 5. Common lead field. Points represent data of Table II. Curves are plotted on the basis of
step-differentiation model with constants assumed as shown.
56
1
206
57
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o
CVJ
O
CVJ
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CD
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ID
o
o
ro
o
CVJ
o
Figure 6. Total lead composition field showing normal common lead field, together with several
samples falling outside the normal field. Sample numbers shown with the points
correspond to those of Table II.
58
sentation are that (1) the variations of the three variables may be simultaneously
/
displayed and (Z) in this particular case, the variations are independent of the
204
uncertainty in Pb , to the first order.
204
Although the uncertainty in Pb introduces a larger error than that
associated with the remaining lead isotopes, it is nevertheless necessary to
204
consider the variations in isotopic composition with reference to Pb as well.
A convenient and useful representation is shown in Figure 7, where the ratios
DK207/Dk204 , 208,^204 , . . . , .. 206 204
Pb /Pb and Pb /Pb are plotted against the ratio Pb /Pb for
each sample.
For both the plots in Figures 5 and 7, samples of very similar composition
have been averaged together and are represented by one point. That the
variations in composition are more or less regular is evident from inspection
of both diagrams. In Fig. 7 in particular, it is seen that as Pb^^/Pb^^
207 204 208 204
increases, Pb /Pb and Pb /Pb increase regularly, with the latter
"curve" showing the greatest gradient. The curves that appear in the graphs
show possible correlation of the variables with time, as discussed in following
sections .
44
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40
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38
37
36
35
34
33
32
31
30
29
28
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17
16
15
14
13
12
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6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24
204
Plot of ym and zm against xm. Points represent data of Table II,
nd curves are plotted on the basis of the step-differentiation model
rith constants assumed as shown.
60
Age Relations for Various Earth Models
The interpretation of lead abundances pertaining to events in earth history
must necessarily depend on the model proposed to represent the time dependence
of the isotopic abundances of rock lead. A simple model, herein referred to as
the step -differentiation model, requires the complete differentiation of the crust,
essentially into its present form in a very short time interval subsequent to the
accretion of the planet. Another possible model would involve a continuous
differentiation of the earth's outer shell with time. A general expression for
the rate of differentiation would assume some exponential relationship involving
a decreasing rate of differentiation from the time of formation of the earth.
Least likely would be a model involving a maximum in the differentiation rate
or an increase with time.
Derivation of Step- Differ entiation Model
206 238
Consider the production of radiogenic lead Pb from U in a given geo
chemical environment in a permanent crust. If, for convenience, time t is
measured positively back into geologic history from the present, then the
differential equation for uranium decay may be written
238 238
dN = XN dt
(17)
238 238
where N is the number of U atoms at time t in the specified environment,
2 38
and X is the decay constant for U . Specifically, the variation of the ratio of
238 204 204
N to N , the number of Pb atoms, is required and if it is assumed that
204 .
N is constant with time, equation (17) may in turn be written
dP * XPdt
(18)
61
^ ^ g ^ Q y|
where P s N /N . Integrating equation (18) and taking P s PQ at t a o , one
obtains
P = P0 e Xt .
(19)
Using similar notation the differential equation for variation of x s
where is the number of atoms of Pb^*^ in the designated matrix,
dx a - XPdt
(20)
Substitution of the explicit time dependence of P from equation (19) gives
dx = - XP0 e ^dt
(21)
Integration of equation (21) yields
X * -PoeU + C,
(22)
where C is the constant of integration.
Depending on the boundary conditions specified to determine C, equation
(22) may be reduced to several final forms. Two sets of boundary conditions
are most commonly used, (a) At t = o (present time) x » 0(o, the presently
observed value of in the crustal environment under consideration.
<*0 + whereof is the primeval or initial ratio of at
time t = tc (time of earth formation = time of crust formation according to
this model), = N /N due to production of radiogenic Pb^^ in this
matrix throughout geologic time. Equation (22) then becomes
x =0(o - PQ(eXt - *)• (23)
(b) At t a t , x = Of . For this case equation (22) reduces to
o c
*Xtc Xt .
xs<Xc + P0(e - e ) (24)
The exact significance of t in equation (24) depends on the particular
c
cosmogonical theory invoked to account for the origin of the solar system and
of the earth in particular. According to a currently accepted view the earth
62
initially accreted from undifferentiated matter very similar in composition to
meteoritic material. Increased temperatures at the surface possibly due to
impact during the late stages of planet formation caused the differentiation of
a thin basaltic layer (5 km)now preserved under the ocean sediments. Subsequent
differentiation produced the iron-nickel core and the granitic continental layer s .
The step-differentiation model requires all of this differentiation to have occurred
in a short time interval close to the formation of the earth.
The composition of meteorites has been fairly well established and of
pertinent interest here is the datum that the lead to uranium ratio is of the
28
order of 80:1 in average meteorites (obviously for t =o|. Assuming that
9
the age of meteorites is roughly that of the earth, i.e. 5 x 10 years, then the
initial lead to uranium 238 ratio was approximately 40:1. Noting that the present
29, 30 .
ratio of lead to uranium in the most mafic rocks measured
is about 10:1,
204
it is seen that the rate of accumulation of radiogenic lead relative to Pb in
primordial material was about one fourth that of the slowest rate observed in
present crustal rocks. Or, stated alternately, the increase in the ratio of
O1206 204
in meteorites from t = t£ to t = o could not exceed 2%.
On the other hand, in an environment such as the present basaltic or granitic
crust the rate of generation of radiogenic lead would be sufficient to change the
isotopic composition of total lead by a readily measurable amount in the period
of earth history, t is therefore understood as that post- differentiation time
204
remote in earth history at which radiogenic lead relative to Pb began to be
produced in the "crust" at a rate comparable to that in the present crust.
? 0 A 7 04
in equation (24) is the ratio of Pb UD to Pb at time tQ; this lead isotopic
63
composition is called primeval. (For the purposes of this discussion, an arbitrary,
technical distinction will be made between the words " primeval" and "primordial".
"Primordial" is used with reference to the pre -differentiation era, for describing
the earth and its materials in their elemental, accreted form and "primeval" is
associated with an arbitrary post-primordial point of time remote in earth history.)
If a relatively short time elapsed before the assumed step-differentiation took place,
then the primeval lead composition is esentially identical to that of lead, assumed
to be primordial, found in meteorites.
It may be observed that equation (24) does not necessarily imply the existence
of a solid crust at time t . Although the existence of a solid crust at that time is
c
very probable, equation (24) merely requires the existence and continuation of a
crust with a geochemical composition comparable to the present crust.
2-11
Discussion in the literature
on the significance of o(, and t is often vague,
c c
and the definitions stated here are not necessarily identical with those of the
previous writers. The present definitions are made to promote maximum clarity
for the considerations at hand.
Turning to the geochemical processes of lead ore formation, the extraction of
lead from a given crustal matrix (source rocks) and the accompanying lead
mineralization at time t (assuming negligible lapse of time between the two
events) terminates the growth curve of the three radiogenic lead isotopes and
"freezes" the isotopic composition obtaining in that environment at time t^.
Each common lead mineral under the conditions assumed reflects an isotopic
206
composition characteristic of its age t , and the Pb composition may be
displayed in equations (23) and (24) as
xm = °<o - po (e
\t
m
- 1),
(25)
64
and
x a
m
<X0 + PQ(eXtc - eXtm).
(26)
In similar manner, equations analogous to(25) and (26) may be derived for the
207 208
isotopes Pb and Pb . Employing typical notation, the two complete sets of
equations are:
xm sC*o " Po (e
Xtm
ym ~f~*o ~ £Po (e
zm = Yo- Wo(e?
X't
m
1)
- 1 )
m - 1 )
(27)
xm=*c + Po<eXtc
ym=^c+£P0(eX'tc-eX'tm)
+ W0(eV'tc -eV'S. (28)
. .. ,t207/,t204 , 208 / xr204
ym and zm are the respective time -dependent ratios N /N and N /N ,
where and are the numbers of atoms of Pb^^ and Pb^^;^0 and yo are
the presently observed ratios N and N0 / NQ respectively. ^3c and
207. 204 208. 204
yc are the respective ratios N /N and N /N obtaining at time tc . E is
the present value of and WQ is the contemporary value of N^^/N
235 232 235 * 232
where N and N refer to U and Th atoms. All quantities refer to the
# 235
crustal environment specified for equation (17). The decay constants for U and
232
Th are denoted by X1 and X", respectively.
If now the values of ao,^, yQ, PQ, and WQ are assumed to be the same in all
portions of the earth's crust which serve as the sources of common lead deposits,
and if it is further assumed that the only change of the lead to uranium ratio
therein is due to radioactive decay, then the use of the isotopic composition of
common lead minerals of known age in equations (28) would permit an accurate
evaluation of tp . Although the actual situation is more complicated than this simple
picture affords, it is worthwhile to make such a calculation to describe a limiting
case. The limitations of the proposed calculation may be clarified by an enumeration
of the implicit and explicit assumptions employed.
Assumptions :
(1) The decay constants V , and V have been constant throughout earth
history, and are reliably represented by the values obtained in the laboratory
today. Moreover, £ is constant throughout the crustal environments considered.
(Z) The amount of equivalent radiogenic lead represented by the unstable
elements lying between the end members of the three radioactive decay series
is at all times negligible once secular equilibrium has been reached.
(3) Each of the three radioactive decay series is closed so that none of the
member elements has been added or removed by extraneous processes throughout
geologic time .
(4) The amount of the radiogenic lead isotopes created or destroyed by
natural processes other than the decay schemes delineated, is negligible. More-
204
over, Pb has not been produced or removed in nature throughout geologic
time .
(5) Uranium to lead and thorium to lead ratios are uniform in zones of lead
extraction.
2 04
(6) The only change of uranium and thorium relative to Pb in the designated
zones of the crust throughout earth history is that occasioned by radioactive decay.
(7) The process of rock lead extraction must involve a complete mixing of
the radiogenic lead and primeval lead present in the rock, and is therefore homo¬
geneous .
(8) The possibility of significant chemical fractionation of the isotopes of lead
66
is negligible for all conceivable thermochemical environments of lead extraction
and ore mineralization.
(9) The time required for both the processes of extraction and mineralization
is negligibly small compared to the time of accumulation of the radiogenic lead.
(10) The time interval between extraction and mineralization of lead is in¬
significant relative to the time of accumulation of the radiogenic lead.
(11) In the process of transport from lead source to site of mineralization,
the ore -carrying solutions are not contaminated by lead of extraneous origin.
(1Z) The amount of common lead minerals and/or radiogenic lead minerals in
the source rocks due to previous mineralizing activity must be small compared to
the total amount of lead involved.
(13) The two sets of constants cXq, p Q , and o£c, ^ c are constant in the
portions of the crust involved in lead ore formation.
Insofar as the assumptions are not met, the validity of the application of
equations (27) and(28) to common lead minerals of diverse origin can be questioned.
It is virtually certain that conditions (1), (2), (4), (8), (9), and (10) are fulfilled
in nature. Assumption (3) is probably valid, but note must be taken of the possible
238
migration of radon (half-life 3 1/2 days) in the U decay chain. The remaining
items merit further consideration and will be discussed later.
67
Comparison of Common Lead Isotopic Data with the Step- Differentiation Model
A qualitative comparison of the data with the step -differentiation model is
exhibited by the curves projected with the data in Figures 5 and 7. The particular
curves shown include the isotopic composition of meteoritic lead reported by
2 8
Patterson , et.al., as the composition of primeval lead. In Figure 5, the
curves enter the bottom of the field for old leads and the compositions move up
along the indicated loci as the age of mineralization becomes increasingly
younger .
The curves represent equations (28), with selected values of the constants
to bring the curves into the domain of the points representing the data. For
28 . n
all cases, the composition of primeval lead referred to is = 9.4, B = 10.3
and = 29.2. For the curves labelled mafic, the values of PQ and WQ are
taken as 7.95 and 32.3 respectively, and corresponding values for the siliceous
curves are 11.7 and 51.1, respectively. These values for PQ and 'WQ are based
on abundances of uranium, thorium and lead in various types of crustal rocks
29 • 30
reported by Evans and Goodman , and Sendell and Goldich , using the
31
modern common lead abundance of Quaternary sediments reported by Patterson ,
204
et.al., to obtain the amount of Pb in contemporary rock lead. The remain¬
ing pair of curves designated as "average of lead sources" is plotted with PQ = 9.92
13
and WQ *3 38. 3, which are values reported by Collins , et.al., as the average
required for a least squares fit of a number of common lead minerals to the
9
primary earth model. The values of t employed range as shown from 4.0 x 10
yrs. to 4. 5 x 10^ yrs. The values used for the constants £, X, X’, X", are those
32
reported by Fleming, Ghiorso and Cunningham
For the curves in both Figures 5 and 7, the terminal point at the upper end
68
of each curve represents modern lead composition obtainable with the given
parameters. From this qualitative comparison it is seen that, assuming the
validity of equating primeval lead to the meteoritic lead composition reported,
the data may be considered to be generally compatible with the step -differentiation
o g
model for values of t between 4.0 x 107 yrs. and 4.5 x 107 yrs., and with
values of PQ and WQ corresponding to those of siliceous, continental rocks of
the earth's crust.
Least Squares Fit of Dated Samples to Step -Differentiation Model
A more quantitative treatment of the data is obtained by means of a least
squares fit to the equations (27) for the step -differentiation model. Such a
procedure involves, however, the introduction of an added uncertainty, the
geologic ages of the common lead minerals.
Age Considerations
.
The difficulty of assigning reliable ages to common lead minerals necessarily
restricts the analysis to a relatively small number of samples, for which suffi¬
ciently good dating criteria exist. Some 16 Lamont samples have been so
dated and, together with three of the Toronto analyses added to give a more
even spread on the time scale, are shown with the assigned geologic ages in
Table III. The data and evidence for the ages used in this table are contained
in the references.
1
Most of the post-Cambrian samples are dated from position in the strati¬
graphic column, since the errors involved although large percentage -wise, do
not have a pronounced effect on the constants determined by least squares
analysis. For one or two post-Cambrian samples, such as no. 117 from
Henderson, N.C., for example, ages of radioactive minerals of contemporary
L
69
Table III
Ages For Common Lead Minerals
No.
Source Locality
I s o t o p
(Pbz
206
i c C o m p o
04=i. oo;
207 '
s i t io n
208
Geologic
Age
(in m. y . )
43
cl
Ute Mine, Hinsdale Co., Colo.
19.03
15. 74
38. 53
1 5± 10
120
Casapalca, PeruL‘
18.85
15. 76
39.23
2 5±1 0
119
Q
Durango, Mex.
19. 12
15.92
39.20
2 5±10
133
Laurion, Greece^
18.80
15.67
38.99
70±20
111
p
Phoenixville, Pa.
18.75
15.71
38.83
120±30
98
(
Middletown, Conn.
18.64
15.83
38.94
1 70±1 5
82
Kellogg Mine, Ark. ^
18.61
15.69
38.78
200±50
97
Fallon Quarry, Quincy, Mass.
18.41
15.75
38.43
230±40
117
Henderson, N.C.1
18. 58
15.78
38.82
340±20
C(10)
Katanga, Belgian CongoJ
17. 58*
15.94*
38.34*
630±30
115
Franklin, N. J.
17. 15
15.49
38.25
700±200
18
Sault Ste . Marie, Ont. *
17.79
15.92
37.70
700±300
21
Mountain Pass, Calif . m
16.26
15. 55
36.34
925±200
137
Broken Hill, N.S.W.n
16.27
15. 56
36.37
1, 200±300
4
Great Bear Lake, N.W.T.^
16. 13
15.43
35.75
1, 450±1 00
129
Fahlun, Langban, Sweden0
15.86
15. 58
35. 74
1, 600±200
130
C(15)
Great Slave Lake, N. W. T J
14.63*
15.27*
34.46*
1, 900±300
8
Ace Mine, Goldfields, Sask.1
" 14.36
14.96
34.49
1, 900±100
C(1 7)
■j •
Sioux Lookout, Ont.J
14. 05*
14.92*
33.85*
2, 600±500
a W. Lindgren, Mineral Deposits, p. 499-508, New York, 1933
J. D. Irving and H. Bancroft, Geology and Ore Deposits near Lake City, Colo.,
U.S.G.S. Bull. 478, p. 87-95, 1911
70
Table III, Continued
k Geological Staff of Cerro De Pasco Copper Corp. , International Geological
Congress, Report of 18th Session, Part VII, Lead and Zinc Symposium,
pp. 180-185, 1948.
H. E . McKinstry and J. A. Noble, Economic Geology 27, pp. 501-522, 1932.
c W. Lindgren, op. cit. , pp. 598-600.
B. Prescott, Trans. Am. Inst. Min. Eng., 51, pp. 57-99, 1916.
^ G. Marinos, The Ores of Lead and Zinc in Greece, 18th International Geological
Congress, loc. cit., pp. 308-313.
F. Beyschlag, J.H.L.Vogt and P.Krusch, The Deposits of the Useful Minerals
and Rocks, Vol. 2, pp. 746-749, Trans, by S. J. Truscott, MacMillan Co.,
London, 1910.
e F. Bascom and G. W. Stose, U.S.G.S. Bull. 891, pp. 123-125, 1938.
r
T. A. Cook, Geology of Conn., 1933, Hartford, Conn.
W. G. Foye and A. C. Lane, Correlations by Radioactive Minerals in the
Metamorphic Rocks of Southern New England, Am. Jour. Sci. Vol. 28,
pp. 127-138, 1934.
Q
J. C. Branner, Annual Report, Vol. V, Ark. Geological Survey, pp. 9-35, 1892.
H. F. Bain, U.S.G.S., 22nd Annual Report, Part 2, p. 133, 1901.
h
B. K. Emerson, Geology of Massachusetts and Rhode Island, U. S . G. S . Bull. 597,
1917.
M. P. Billings, Pegmatites of Massachusetts, Coop. Geologic Project, Bull.
No. 5, Mass. Dept, of Public Works and U.S.G.S., 1941.
C . H. Warren and C.Palache, The Pegmatites of the Riebeckite -Aegerite Granite
of Quincy, Mass., Proc. Am. Acad, of Arts and Sciences, 47, pp. 125-168, 1911.
W. G. Foye and A. C. Lane, Correlations by Radioactive Minerals in the
Metamorphic Rocks of Southern New England, Am. Jour. Sci., Vol. 28,
pp. 127-138, 1934.
W. R. Eckelmann and J. L. Kulp, The Uranium-Lead Method of Age Deter¬
mination, submitted to Bull. G.S.A., 1955.
^ A. O. Nier, The Isotopic Composition of Radiogenic Leads and the Measurement
of Geological Time, II, Phys. Rev. 55, pp. 153-163, 1939.
71
Table III, Continued
J. L. Kulp, G. L. Bate and W. S. Broecker, Present Status of the Lead Method
of Age Determination, Am. Jour. Sci. 252, pp. 345-365, 1954.
C.B. Collins, R. M. Farquhar and R. D. Russell, Isotopic Constitution of
Radiogenic Leads and the Measurement of Geological Time, Bull. G.S.A. 65,
pp. 1-21, 1954.
A. W. Pinger, Geology of the Franklin-Sterling Area, Sussex Co., New Jersey,
18th International Geological Congress, lco. cit. , pp. 77-87.
^ H. C. Cooke, Regional Structure of Lake Huron-Sudbury Area, Symposium:
Structural Geology of Canadian Ore Deposits, Jubilee Volume, Canadian Inst,
of Min. Met., pp. 580-589, 1948.
mPrivate communication, P. S. Barton, Geology Dept. , Columbia University.
n F. C. Andrews, Geology of Broken Hill, New South Wales, 18th International
Geological Congress, loc. cit., pp. 187-194.
° N. H. Magnusson, Zinc and Lead Deposits of Central Sweden, 18th Inter¬
national Geological Congress, loc. cit., pp 371-379.
* Analysis by Collins, et. al. , reference 13.
General References:
J. Rodgers, Absolute Ages of Radioactive Minerals from the Appalachian Region,
Am. Jour. Sci. 250, pp. 411-427, 1952.
A. Holmes, The Construction of a Geological Time Scale, Transactions of the
Geological Society of Glasgow, 21,. pp. 117-152, 1947.
72
mineralization are used. Radio-isotope ages are considered much more reliable
than those obtained by the usual non -quantitative geologic methods and it is un¬
fortunate that more such ages are not available.
For the pre -Cambrian samples, the inaccuracies of geologic dating become
increasingly intolerable, and where possible these samples have been assigned
ages from radio -isotope data on minerals of supposed contemporary mineral¬
ization. For fou~ samples however, no. 115 from Franklin, N. J., no. 18 from
SaultSte. Marie, , Ont. , no. 137 from Broken Hill, N.S.W., and nos. 129 and
130 averaged from Fahlun and Langban, Sweden, no satisfactory radio-isotope
ages for minerals of immediate association exist. The ages shown are those
deduced on the basis of the best geologic evidence obtainable, and do not have
as much reliability as the other minerals.
Of the remaining pre -Cambrian samples, those considered to have the most
reliable ages are numbers 10 from Katanga, Belgian Congo (Collins analysis),
4 from Great Bear Lake, N.W.T., 8 from Goldfields, Sask. , and 15 from
Great Slave Lake, N. W.T. (Collins analysis). Ages assigned on the basis of
radio-isotope data can be very tenuous, if the common lead and radioactive
minerals are not taken from the same deposit. This is illustrated in the case
of the Sioux Lookout sample, Collins number 17. The age for this sample has
been taken as that of the Huron claim pegmatite some 200 miles west of Sioux
Lookout. But there is no guarantee that these minerals were deposited at the
Q
same time. Collins assigned an age of 2.48 x 10 yrs. for the Huron Claim
3 3
pegmatite but a re-evaluation of the data suggests a value of 2.6 x 10^ yrs.
as more probable. The geologic ages assigned to the Broken Hill, N.S.W.
9 9
mineral range from a value of 0.9x10 yrs. assigned by Nier to 1.5 x 107 yrs.
73
13
given by Collins on the basis of age determinations made at Radium Hill.
While Nier's figure appears small, an age of 1 . 5 billion years predicated
upon the assumption of contemporaneity of minerals from different rock
masses is questionable; hence a compromise age of 1 . Z billion years has
been retained here as a first approximation.
For pre- Cambrian samples two factors may contribute to uncertainty
in the age: (1) the uncertainty in the age itself due to re crystallization
33
effects and the loss of lead ; (2) contemporaneity of mineralization is
difficult to establish unless the minerals under consideration come from the
same rock mass. Certainly ages assigned on the basis of province-wide
orogenic activity must be considered suspect.
Mathematical Analysis
The use of least squares analysis for common lead data has been
amply discussed and illustrated by previous writers on the subject
8 11
(see especially Bullard and Stanley , E. McCrady , and Collins, Farquhar
13
and Russell ) .
Employing equations (27) with OiQ, jj>0, y0, PQ and WQ as the parameters
for the least squares fit, the normal equations may be written as
(29)
n/5o-£porJ*l<e
n
nYo ~ wcrrScl(e
(30)
(31)
n
(32)
74
n
n
n
&r^l(eX"tm - ' rn="lZm(e V tm - D - wOn^i<e^ tm ' ^ = °-
A"t
V'tT
,2 _
(33)
n is the number of samples fitted to the curves. The five unknowns may be
solved for as follows:
— —
= ifSLxm+P0X(eXtm - 1)1
11 ym=l m= 1 4
\m® 1 m= 1 J
io
'm
+ W02.(eX"tm - 1)
m=l
1
(34)
(35)
(36)
where P and W have the values -
o o
= ^(2xmlZ(eXtm - 1) - r£* *m<eXtm - 1) + € (Zym)2eVtm - 1)
- nE2ym(eX'tm - !)] -5- {n2(eXtm - l)2 -^(eXtm - lj)2
+ nt2Z(eX,tm - l)2 - £2^(eX'tm - 1)] 21
(37)
w =
o
(Zz m)Z(eX"tm ‘ l) ~ n"£zm(eV tm ~ 1)
n^(eXMtm _ i)2 -][2(eX"tm - 1)] 2
Using the values ӣ = 138, 0. 154 x 10'^ ^ = 0. 972 x 10"^ and
- 9 - 1 32
* 0.0499 x 10 yrs . 1 reported by Fleming, Ghiorso and Cunningham ,
equations (34) through (38) give for the data of Table III the values shown for the
first entry in Table IV. Also shown for comparison purposes in Table IV
are several other sets of values for these constants. The data reported by
1 3
Collins , et.al., are derived from 17 common lead minerals, not all of
which are different from the Lamont samples. The cotunnite from Mt. Vesuvius
is probably the most modern lead "ore" specimen obtainable. It was estimated
by the collector, Dr. B. H. Mason of the American Museum of Natural History,
(38)
to have been deposited within a 36-hour period prior to collection (March 16, 1954).
75
Table IV
Comparison of Modern Lead Isotopic Abundances
and of Values for PQ and WQ
Source
*o
Xo Po
Wo
Least squares analysis of dated
lead ores, this work
18.9
15.9
39.2 11.5
42. 7
Least squares analysis of dated
lead ores, Collinsf et. al.
18.4
15.6
38.4 9.92
38.3
Cotunnite collected from
fumarole at Mt. Vesuvius,
Italy, 1954, our sample 131
19.0
15.4
39.3
Average of lead from Quater¬
nary sediments, Patterson, ^
et. al.
18.9
15.7
38.8
a Collins, Russell and Farquhar, reference 13.
k Paterson, Goldberg and Inghram, reference 31.
The last entry in the table, reported by Patterson and co-workers, is an
average of the values obtained from the manganese nodule and from the red
clay sample.
For further comparison of PQ and WQ, Table V shows values of these quantities
computed for mafic and siliceous crustal rocks from the abundance data of Evans
29 30 34
and Goodman , Sandell and Goldich , and Senftle and Keevil , using modern
lead abundances reported by Patterson^, et. al. It should be observed that the
values of P^ and W determined for Table V suffer from the fact that the lead
o o
abundances are not from the same sets of rocks for which the uranium and
thorium abundances are reported.
The Lamont constants shown in Table IV are in general agreement with the
other values shown and confirm the fact that, on the basis of the step-differenti¬
ation model, common leads have been extracted from a fairly siliceous environ-
76
Table V
Uranium and Thorium to Lead Abundances in Continental Rocks
Rock Type
Uranium
Concentration
Thorium
Concentration
Lead
Concentration
Po
Wo
Acid Igneous
3 . 0±0 . 3a g / ton
1 3±2a g / ton
19k g/ ton
11.8
50.9
Basic Igneous
. 96±0. la
3.9±.6a
9b
7.94
32.3
Granitic
3. 82c
12 . 48c
19b
15.0
48.9
a Evans and Goodman, reference 29
b Sandell and Goldich, reference 30
c Senftle and Keevil, reference 34
ment, as indicated by the values for PQ and WQ, corresponding to those observed
in surficial, continental rocks today. The Lamont values for P and W exceed
1 o o
those of Toronto in particular by about 10%. The composition of modern lead
from our least squares analysis is more nearly in agreement with that reported
by Patterson than the Toronto values. However, it may be argued that Patterson’s
values may not necessarily be expected to agree with those deduced from the
step -differentiation model by least squares analysis.
The abundances of Table III are plotted against age in Figures 8 and 9,
together with the curves for the step-differentiation model, using the constants
determined by least squares fit to the data. In view of the meaning of the step-
differentiation model equations as defined in this paper, it again seems admissible
to equate primeval lead composition to Patterson's meteoritic lead composition.
21
This conclusion has been presented and discussed by Houtermans . If therefore,
the meteoritic lead abundances are read as ordinates on the solid curves in
Figures 8 and 9, the corresponding abscissae give the following values of t
(age of the earth's crust):
77
Figure 8. Plot of xm and ym versus time. Solid curve shows least squares
fit of analyses in Table III to the step -differentiation model.
Dashed curve is plotted with k= .472 x 10 yr s . and jjl= . 62 5 x 10 yr s .
78
0
2 3
Time (I x I09 years )
Figure 9.
Abundance of Pb^08 relative to Pb^^ versus time. Curve obtained
from least squares fit of data in Table III to the step -differentiation
model.
79
tc = 3.9 x 1 09 yr s . ,
tc,= 4.4 x 109yrs.,
tc"= 4.2 x 1 0 9 y r s . , (39)
from the curves Pb206/Pb204, Pb207/Pb204, and Pb208/Pb204, respectively.
An average value t = 4. 17 x 109 yrs. is obtained for the values in equation (39)o
Ideally, the values of t obtained from each of the abundance curves should
be equal. The fact that there is some spread in the values, equation (26),
probably reflects inadequacy of the data, as well as the lack of realization of
some of the assumptions invoked in setting up the step -differentiation model.
It should be emphasized that the evaluation of the constants in Table IV by
least squares analysis does not in itself constitute a validation of the step-
differentiation model, equations (27). The fitting procedure of the least squares
treatment merely determines the best values of the constants for any given
function such that the sum of the squares of the residuals is a minimum. Thus
any information such as the age of the earth's crust, deduced from the step-
differentiation or any other model must depend not only on the adequacy of the
data, but also on the validity of the model itself.
As a final criticism, it must be noted that sufficient data do not yet exist
for a highly reliable least squares analysis with any model. The least squares
method is essentially a statistical analysis, and it follows that the number of
samples should be large. In this particular case, the fit is especially sensitive
to the older samples and it is evident that a much larger number of old pre -
Cambrian samples is needed. The dependence of the results on the older samples
may be illustrated by varying the age of the oldest sample, Collins no. 17 from
14
Sioux Lookout. In a re study of common lead ages, Allan, Farquhar, and Russell
80
have obtained a new value for the age of the Sioux Lookout mineral by a math¬
ematical procedure which does not utilize geological ages of pre-Cambrian
common leads. The age so obtained is 2.31 x 10^ yrs. If now this age is
associated with the Sioux Lookout sample, the equations (34) through (38) give
the following new values for the constants:
<*o= 18.9
o= 15-8
o= 29.2
y0= 12.4
WQ= 45. 2
Comparing with the original constants in Table IV, 0(o, j}Q, ^ Q, have not
changed appreciably, whereas Pq and Wq have increased by almost 10%. The
average value t , obtained with the new constants, equation (40), is t = 3.98
c c
X 109
yrs. , a change of nearly 5%.
While the foregoing illustration represents an extreme case, it is never¬
theless evident that in order to minimize the effects of error in any one given
sample, it would be desirable to both decrease the possible uncertainty in age
of old leads, and to increase substantially the number of dated common lead
m°
(40)
minerals with large t
81
Model Embodying Continuous Differentiation of the Earth's Crust
Consider a model which allows for continuous differentiation of the crust,
from an original primordial composition represented by chondrites, to a
siliceous composition characteristic of granitic rocks today. The evidence
for a step-differentiation is not altogether conclusive and moreover, with a
proper analytical representation, the discrete differentiation should be
contained in the continuous differentiation formulation, at least as a limiting
case, if the boundary conditions so require.
Although differentiation of the whole crust is loosely referred to, the
particular differentiation here designated is the change in geochemical
composition of potential lead ore source material, and even more specifically,
in the uranium to lead ratio of that material. Other portions of the crust
are not directly involved, although it is conceivable that complementary
changes were taking place simultaneously throughout the whole crust, or
what was to become the crust.
The differentiation hypothesized does not distinguish between migration of
uranium and/or lead from the mantle as opposed to changes within the crust
(i.e., above the Mohorovicic discontinuity) as it is now known. The formula¬
tion merely admits of an open system and no specification is made as to the
origin or destination of uranium and/or lead entering or leaving the system.
It is quite likely, however, that since most of the earth's lead is below the
Mohorovicic discontinuity and uranium is above it, some transfer between
crust and mantle is involved. There may be superimposed additional effects
of intra-crustal differentiation. Either or both effects are compassed within
the proposed formulation.
82
It is to be emphasized that the geochemical composition of the environment
of ore lead sources considered is correlated with time, rather than the
amount of a given type of differentiated material with time.
Not many criteria are available to determine the proper generating
function for the differentiation process. From the uranium to lead ratio
found in rocks of varying SiC>2 content, it is generally observed that the
13 /Pb greatly increases from material of chondritic composition to those of
granitic composition. Since therefore, old rocks of granitic composition
are known, it would seem that the generating function is properly exponential
in nature, with the high-gradient portion of the curve at the old end of the
time scale. Also, if the differentiation reaction proceeds at a rate propor¬
tional to the inequilibrium concentrations, then an exponential dependence
on time is not unreasonable. These arguments are not conclusive, but
merely point to the exponential relationship as presently more plausible
than other general expressions available.
The proposed function is qualitatively illustrated in Figure 10, where
variations in the U/Pb ratio are projected against time. Also shown is the
relationship postulated for the step-differentiation model. The effect of the
decay of uranium is not included for the curves shown.
With the foregoing considerations in mind, the differential equation for
238 2 04
the U /Pb growth curve may be written as
dP s \P - ke^ , (41)
dt
where the generating function, ke^ , is quite arbitrary, beyond the exponential
nature just noted, k and p are constants to be determined and the remaining
83
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
/
i
i
I
i
I
i
i
i
i
i
i
I
I
l
i
LU
O
O
LU
O
O
2
O
H
<
h*
Z
LU
o:
LU
Li.
Ll.
Q
<
H
Z
LU
or
LU
Ll
Ll.
o
CT)
ID
o
3
CL
LU
L—
CO
O
O
J - — - - -
aqi ||9qs ja^no uj
Figure 10. Schematic illustration of possible variation of uranium to lead ratio in outer shell of earth
with time for the models indicated, due to differentiation alone (effect of radioactive decay
not included). The right terminal points of the curves are presumably at or near the
beginning of earth history.
84
symbols are as previously defined. Since time is again measured positively
back into earth history from the present, the generating function must provide
negative increments with increasing t; therefore, with the minus sign shown,
k must necessarily be a positive number.
If the Laplace transformation of P (t) be denoted by P (s), then the Laplace
transformation of equation (41) may be written as:
P(s) =
o
( s-\)
k
v^y
[ (i -TT '
where the initial boundary condition P = P at t = 0 has been incorporated,
o
and s is the complex variable. The inverse transformation of equation (42)
(42)
immediately gives as the desired solution P (t),
P =PQe
Xt
U-|D
[eXt - e^]
206 204
The corresponding growth curve for Pb^ °/Pb may be obtained by
(43)
inserting P (t) from eq. (43) into eq. (4):
dx = -XPdt = -XPQeXt+ kx feXt - e^1]
and direct integration yields
x= -PQeXt +
jeXt- X + C
• r*
( X- |jl) L F
The constant of integration C may be evaluated by applying the condition
(44)
(45)
x =0(o at t = o, and the growth curve may then be written
x
= «v -P (eXt - n + k eXt +
o( ' v^rr
r l1
(X-fi.)
1.
235 204
For the case of Q = N /N , the differentiation process would be
238 2 04
expected to be the same as for U / Pb , since both nuclides have the
(46)
same chemical properties, and possible chemical fractionation effects are
probably negligible. Allowance must be made, however, for the difference
in abundances of the uranium isotopes. An average value may be employed
85
but the exact time dependent ratio of the isotopes introduces no great
complication. The differential equation may therefore be written as
dQ = X'G -
cTE
£ k
ut
e
(X-X’)t
-W- e
(47)
Z 35 Z 3 8
where the present ratio of U to U 0 is denoted by 6, and jjl and k
are the same quantities appearing in eq. (41). If again &<t>l = Q(s).
indicates the Laplace transformed function, then the Laplace transforma¬
tion of eq. (47) may be written thus (with Q=Q0 at t=o):
£k
Q(S) = _!££_ _
(s-V) (X-(i)
U
X’) [s - (|X-X + X1)]
I
yields the required solution Q(t):
□ = Q0e
X't _ £k
(X-p)
(p- X+X' )t
207
The differential equation for y = N may now be written as
N204
dy = -X'G0eVtdt+ i>JL-feVt-e^MV)t] dt
(X-(i) L
Integration of eq. (50) and evaluation of the constant of integration as
before gives
y = |3o - Qo (evt - l) +
£k
X’t
(X-p)
+
(p-X+X1) ^ p)
X' (p-X+X')t|
rrrr J
(48)
(49)
(50)
(51)
In the case of Th^^/Pb^4, the same differential equation will apply
as for U^2^/Pb^4, except that constants k" and p" will not necessarily
equal those used for uranium. With this difference the equation obtained
for W = Pb208/Pb204 is identical in form to eq. (46). Applying the results
to common lead of composition xm, ym, zm mineralized at time tj^, the
86
the equations for the three isotopes may be written thus:
: = oc - P. (e
m ^o o '
y
m
A
Xtm
- 1) + - e
Xt
(X-p)
[
m + k ll _ \ e
L (x-p)
X't
q (eX tm_ 1) + £> _ e m
° (X-p)
(52)
+
£k
(p- X+X' )
t
(P-X+X')t
Tx rpf
z = v - W (eX',t:m 1) + _ k
»o o' - '
m
( V’-m-”)
_X"t
e m + k
]
X" e^1
I !
(X"-|1")
i
It should be noted that the equations (52) representing the continuous
differentiation model involve only the changing ratios of uranium and thorium
to lead. Only insofar as these quantities serve as an index of general crustal
differentiation can the results be generalized to speak of the crust as a whole.
Moreover, the equations are limited to zones in the crust that serve as lead
sources, but again the implications are probably more general. With the
exception of the differentiation allowed for, the assumptions previously
delineated for the step-differentiation model must also hold for equations (52).
The evaluation of the constants k, p and k", p" presents some difficulty.
A rigorous application of the method of least squares is not feasible since
simultaneous equations are involved with the unknowns in exponential and
other non-linear functions, and exact analytical solutions are very difficult,
if not impossible, to obtain.
Although approximation methods are applicable the number of mathematical
operations becomes extensive. In view of the fact that the constants are
dependent on the pre -Cambrian samples to an even greater extent than with
the step-differentiation model, the effort required to evaluate the constants
was not considered warranted because of the small number of dated pre-
Cambrian samples available.
87
A somewhat different approach permits the evaluation of k and p
together with a simultaneous evaluation of t , where t is the time at
P p
which terrestrial lead has the isotopic composition of meteoritic lead,
and the uranium to lead ratio has the primordial value reported by
28
Patterson , et al. If P , Q (X and |3 are the values of the ratios of
P P p rp
tt238 tt235 206 , 207 . 204 .
U , U , Pb and Pb to Pb respectively, obtaining at time
tp, then the foregoing conditions may be analytically represented by the
following equations:
P = P PUP - k '
[eUp e^pl
(53)
P ° X-p
L 1
' Q°-' ‘r- , 1
[eVtP . e(|i-UV)tP
i
(54)
°<p xo<o ' Po<eXtp ' X) +
k ~xtr + v r i
X
etltp](55)
(x-p) -pr L
(x-p)
(3p =^o - Q0(eVV- l) + -f^r)eVtP
(56)
+ _£k _ r V >-x+x')tp]
(p-X+X') l (X-p) J
It will be observed that these equations are simply those of the growth curves
of the continuous differentiation model, equations (43), (49) and (52), with
the appropriate values of the variables inserted.
The assumptions inherent in equations (53) through (56) should be noted:
(1) the isotopic abundance of lead at t is that now observed in iron-meteorites
Jr
( negligible U and Th ); (2) the total uranium to total lead ratio in the earth
at the time of its formation t , may be equated to that now found in stony and
iron meteorites in their proper proportion; (3) the rate of differentiation has
decreased exponentially since the time of planet formation. These assumptions
are listed in order of decreasing certainty. They are all sufficiently reasonable,
88
however, to warrant calculation of the model.
The unknowns k, jjl and t may be found by simultaneous solution of
any three of the equations (54) through (56). The values of and |30
employed are derived from the step-differentiation model (Table IV) by
least squares analysis of the lead ore data. Their use here is justified
not only by the agreement with the Patterson's Quaternary lead abundances
and with the Vesuvius abundances, but also by the fact that the two models
become essentially identical for small (modern) values of t . The value
of PQ is taken from Table V for acid igneous rocks, and is very close to
those in Table IV. The values of PD and O are obtained from the primordial
F p
Z 8
lead and uranium abundances for meteorites reported by Patterson , et al.
by correcting for the natural decay of uranium in time t . We have,
Jr
therefore :
o( a 18. 87
o
po "
15. 77
PQ = 11. 76
a 138
°<p =
Pp =
9.41
10.27
P^ = . 6 186e
X.tp
Qp
\t_
. 00451 5e P
With the values shown in equations (57), a graphical solution of the three
equations (54), (55) and (56) gives the following values:
tp = 5.28 x 10^ yrs.
-9 -i
jjl = . 625 x 10 yrs.
k = .472 x 10 ^ yrs.
(58)
89
That the four equations (53) through (56) are compatible is indicated by
the fact that a graphical solution of an alternate combination, equations
(53), (55) and (56) gives a value of t equal to that of the first combination,
ir
equations (58), to within less than a percent, with a somewhat larger
divergence in the values of k and p, .
It should be noted that the values of k, jjl and t^ obtained in equations
(58) depend only indirectly on the isotopic composition of lead ores,
inasmuch as the values of °C0 and j3Q from Table IV were the only ones
incorporated which depended in any way on common lead minerals.
Because the continuous differentiation model allows for an increase in the
uranium to lead ratio with decreasing t, it follows that in view of the fixed
ratio postulated for step-differentiation model, the derived value for t
ir
should be larger than any previously obtained. If therefore the three
assumptions initially noted are valid, tp = 5.3x10^ years may be regarded
as an upper limit for the age of the earth.
The growth curves for Pb^^ and Pb^^ relative to Pb are shown
as the dashed curves in Figure 8, using the values of k and jjl in equation
(58).
The curves for the two models are identical for small values of tm, but
begin to diverge at about 2 billion years. The divergence becomes larger with
- 9 - 1
increasing values of tm. For the value of p. » .625x10 yrs. , the
corresponding differentiation "half-lifed1 is about one billion years. If the
differentiation of uranium serves as an index of differentiation of all crustal
material, then it follows that the major portion of the general differentiating
forces was expended in the first billion years plus of earth history.
90
If at the end of this period, a sufficient amount of siliceous material was
segregated in the outer shell so that the existence of a crust at that time
could properly be spoken of, then it is seen that the age of the crust so
obtained would correspond roughly to that obtained with the step-differentiation
model, of the order of 4 billion years.
91
Comparison of Lead Isotope Constants and Age Derivatives with Previous Results
Values forOQ., |3>c, ^c, isotopic composition of primeval lead in the earth's
crust, for o<p, p^, primordial lead isotopic composition, for tc> age of the
crust of the earth, and for t^, age of the earth, obtained by other investigators
are summarized for convenience together with those of the present work in
Table VI.
Table VI
Values for Age of the Earth and its Crust and the
Isotopic Composition of Primeval and Primordial Lead
‘c or tp
Primeval or
Primordial Lead Composition
Author
(1 x 10^ yr s . )
*c, p
Pc, p
)c,p
S. K. Gerling^
3.23
- - -
- - -
— -
F. G. Houtermans^
2.9
1 1. 52
14. 03
31.6
c
A. Holmes
3.35
1 0.95
13. 51
- - -
7
H. Jefferys , corrected
Q
by A . Holme s 7
2.87
- - -
- - -
— — -
E. C. Bullard and
P. Stanley^
3.29±.2
1 1 . 86±1 . 47
13. 86±. 56
- - -
C. B. Collins et. al.
3. 5
11.33
13. 55
31. 10
_ _ 33
C. Patterson
4. 51 - 4. 56
9 .41
10. 27
(29. 16)
2 1
F. G. Houtermans
4. 5±. 3
(Patter son1
assumed)
s meteoritic
lead composition
This research
4.2 - 5.3
(Patterson1
assumed)
s meteoritic lead composition
In addition, it may be noted that Alpher and Herman^ have assigned an
upper limit of 5. 3 x 10^ yrs. for t by computing the age required for x^ = o,
92
and McCrady1* has similarly obtained an upper limit of 5.07 x 10' yrs.,
required for y = o. Both of these results are based on the Nier data. The
J m
new data presented in this paper do not significantly affect these maximal values.
It is evident however that the validity of these limits rests on a constant
uranium to lead ratio throughout earth history, such as is embodied in the
step-differentiation model. If the possibility of differentiation effects with
time are allowed for, it follows that the numbers obtained by Alpher and Herman ^
and by McCrady cannot be properly regarded as maximal values.
A survey of the methods used to obtain the data shown in Table VI reveals
that with the exception of the continuous differentiation model of this research,
all have been obtained on the basis of the step-differentiation model, used in
one form or another. Patterson's values for t (4.5 and 4. 6 x 10^ yrs.) were
obtained by calculating a Pb^^/Pb^^ age for the radiogenic lead remaining
after subtracting meteoritic lead from modern oceanic and basaltic leads. Due
to the possibility of the system being open (i.e., allowing for differentiation
effects with time, for example), the Patterson ages must be regarded as minimal,
as he indicates. Patterson's rrieteoritic, modern oceanic and basaltic lead
compositions are an important contribution to the study of earth history, and
his method of caluclating the age of the earth has the additional merit of
averaging secondary changes of rock lead composition due to such possible
phenomena as multiple orogenies, cycling through the sedimentary process, etc.
A brief inspection of the results tabulated in Table VI indicates that the data
may be classed in two groups: group 1, consisting of the first six entries, for
which tc ranges from 2.9 to 3.5 billion years, average 3. 2 billion years, and
the values for o<c, |3C and ^c, averages 11.4, 13.8 and 31.4 respectively, are
substantially larger than those for meteoritic lead; the last three sets of data
93
constitute group Z and the ages here are higher than those in the first group by
at least a billion years.
Of the methods used to obtain the first group of results, that of Holmes is
the most elaborate, but as Bullard and Stanley point out, uncertainties persist
because the same data are repeatedly used in different combinations. The
treatment by Bullard and Stanley is probably the most rigorous, if the propriety
of their sample selection and the validity of their statistical assumptions be
granted. The results of Collins, et.al, are obtained by the method of Bullard
and Stanley with additional data, and have therefore a correspondingly increased
reliability. It is important to note, however, that in spite of differences in the
treatments, the results of the first six authors indicated in Table VI are in broad
agreement. It may be stated here that the Lamont data, if treated by the same
methods employed in the first group, would give substantially the same results
indicated in this group.
The higher age values characteristic of group Z must be attributed to the
incorporation of meteoritic lead composition, which is used in all three methods
for primordial lead isotopic composition. The younger age of 4.Z billion years
resulting from this work and Houterman's result were obtained by using lead
ore data to determine points on the young portion of the age curves model and
are in general agreement with Patterson's values.
The most convenient explanation of the two sets of differing ages, on the
basis of the present work, is that the crust was not formed in a negligibly small
time, but there was required an extended time of the order of a billion years,
as embodied in the continuous differentiation model, in order for a siliceous
outer crust to be built up. As noted previously, this model was shown to admit
an age of 5. 3 billion years for the time at which meteoritic lead composition
94
obtained. From the dashed curves of Figure 8, the mean values of<tfc and j3c
for group 1 of Table VI give an age of about 3.6 billion years, which agrees
roughly with the mean value of tc> 3.2 billion years, for said group. Thus
the continuous differentiation model gives a comparable age for the crust if
the average of the lead isotopic compositions of group 1 is taken as the primeval
lead isotopic composition prevailing in the early crust.
The idea of growth of the earth's crust in time is in itself not new. A
hypothesis embodying the growth of continents has been advocated by J. Tuzo
3 5 36
Wilson ’ . The possible relations between the continuous differentiation
model and Wilson's hypothesis are evident, but it should be borne in mind that
the model deals with the geochemical composition of the crust as a function of
time rather than amounts and distribution of crustal material with time.
It is evident that a precise definition of the age of the earth on the basis
of common lead isotopic compositions is not yet possible. This is due
primarily to the uncertainty in the nature of the required model and the lack
of well dated samples older than 2 billion years. The assumption that the
isotopic composition of lead in the metal phase of meteorites is the same
as that existing in the primordial earth has been questioned but is one of the
most likely postulates in this problem.
On the basis of the preceding summary it is reasonable to believe that
9
the age of the earth lies between a minimal figure of 4. 5 x 10 years
determined by Patterson"^ and a maximal value of 5. 3 x 10^ years as
presented in this work.
95
The actual value may be regarded as depending primarily on the
nature and time required for the geochemical differentiation which
produced the earth's crust. Some evidence for a certain amount of
differentiation at the time of formation of the earth, together with
preliminary calculations for young ore leads of low radiogenic lead
content indicates an age closer to the minimal value. Tentatively a
best estimate of the age of the earth may be placed therefore at
4.8±.2 x 10^ years.
96
Regional Analysis of Common Leads
The large number of isotopic analyses completed in the course of
this study adds considerably to knowledge of the regional variations of
the isotopic composition of lead from common lead minerals. In a
crude way the isotopic composition of samples from various localities
follows an "age curve", i.e., a smooth curve of isotopic composition
vs. age can be drawn which is closely approximated by a considerable
number of the samples. On the other hand there are many samples
which do not conform to this "normal" behavior and are termed
"anomalous". Such variations are not unexpected. Significant
differences in uranium and thorium to lead ratios are known. Most ore
lead presumably originates from a fairly small volume element of the
earth's crust, thus reflecting the local environment of origin. Thus in
terms of the models previously discussed, PQ and WQ are not truly
constants .
The distribution of samples from North America is shown on the map
of Figure 11 . The majority of samples analyzed in this work are from the
N rth American continent, and cf these the largest group is from the
districts of the Mississippi Valley, as shown on the map. The majority
of younger minerals are found in lead-zinc ore deposits associated with
sedimentary rocks while the older samples are found in a metamorphic
or igneous environment. Three samples (nos. 19, 97 and 117) are of
pegmatitic origin.
97
MISSISSIPPI VALLEY DISTRICTS^
1. Upper Mississippi Valley District
2. Central Missouri
3. South-East Missouri District
4. Southern Illinois - Kentucky District
5. Tri - State Region
6. Northern Arkansas
Figure 11. Map of North America, showing sources of samples. Samples in
Mississippi Valley districts : distr. 1, 12 samples; distr. 2,
1 sample; distr. 3, 8 samples; distr. 4, 2 samples; distr. 5,
14 samples; distr. 6, 2 samples.
98
It would be very useful to establish possible regional variations of
P and W . and this could be done if the ages of the samples were
o o’ 0
accurately determined. However, for most samples, the uncertainty
in the age more than accounts for the displacement from the time curve,
and it is therefore not possible to obtain sufficiently reliable information
to establish broad patterns.
The so-called anomalous leads may be divided into three basic
groups: (1) the Joplin type, (2) the Athabasca type, and (3) the Ivigtut type.
1
(1) Joplin type. This group, first identified by Nier , is
representative of the Mississippi Valley leads in general and a number of
206 207 208
other leads. It is characterized by an excess of Pb , Pb and Pb
over that expected from the age curve.
Virtually all the leads from the Mississippi Valley region show this
anomaly. The high radiogenic content is not obtainable with reasonable
values of the constants from any of the proposed models of crustal history.
The ages of these deposits are generally no younger than Cretaceous and
yet more radiogenic lead is contained than in modern leads (t^s o).
To the south in Central Arkansas and to the east in the Kentucky- Tenne s see
district the anomalous character of the leads becomes much less pronounced
and even disappears. Other leads which have a similar anomalous composition
are: no. 14 from Eganville, Ont. ; nos. 24 through 28 from Minnie Moore
Mine, Bellevue, Id. ; nos. 86 through 89 from Kentucky and Tennessee as
borderline cases; no. 96 from Newbury, Mass.; no. 113 from Friedensville ,
Pa . , as a borderline case ; no . 116 from Hunterdon Co . , N. J. ; nos . 12 7 and
128 from Hungary and Germany, respectively; and no. 132 from Trepca,
99
Yugoslavia. This type of anomalous composition is discussed separately
under Mississippi Valley leads.
Sample no. 17, from the Worthington Mine, Sudbury, Ontario, is an
exaggerated case of the same type anomaly as the Mississippi Valley
leads. However, although its radiogenic content considerably exceeds
that of modern leads it is different from the Mississippi Valley leads in
at least two respects; (1) the deposits are in an entirely different environ¬
ment, in metamorphic rocks that are definitely pre -Cambrian in age:
208
(2) the excess Pb is much larger than that usually found in the
Mississippi Valley leads.
This sample shows that the Joplin type anomaly is not restricted to
young leads but may have developed at almost any time in earth history.
The Sudbury deposits have been subjected to detailed studies utilizing
1 5
lead isotopic analyses by Russell , et al, and these authors conclude
that radiogenic lead has been added to normal lead from a source with a
thorium to uranium ratio of 5.2 (measured at the present time).
(2) Athabasca type. This group shows an appreciable excess of only
^ o ^ ^ o y
Pb and Pb^* , thus indicating derivation at least in part, from a uranium-
rich environment. The samples nos. 9 through 13 from the Goldfields,
206
Sask. , region are associated with pitchblende deposits. The high Pb
207
and Pb concentration is due to lead removed from the pitchblende at
the time of formation of the galena (PbS) or clausthalite (PbSe). Recrystalli-
3 8
zation effects in the Athabasca (Goldfields, Sask.) deposits have been shown
100
Study of the Witwater srand deposits3^ indicates that the galena may occur
as small blebs not in "atomic" contact with radioactive minerals. However,
they are of sufficient proximity to the radioactive grains so that recrystalliza¬
tion could mix radiogenic lead with rock and hydrothermal lead in the formation
of the common lead mineral.
206/T^204
(3) Ivigtut type. This group is characterized by low Pb /Pb
Pb^^/Pb^^ Pb^^/Pb ratios compared tothose predicted by the
"age curves". Thus this lead was derived from an environment such that
the Pb/U+Th was higher than that for the "average ore lead
1 1
The Ivigtut, Greenland sample no. 19 indicates an age from the age
curves (compare isotopic composition with model curves in Figures 8 and 9)
which is considerably in excess of the reported geologic age of about 600
million years (late pre - Cambrian) . The Wallace, Id. cerussite, no. 23,
is another Nier sample which is anomalous in the same way There is
some uncertainty as to the geologic age, but if the reported age of early
Tertiary is accepted, there is definite conflict with the isotopic age which
apparently is late pre - Cambrian.
The regional variations in isotopic composition of common leads for
the United States are shown in Table VII, where averages have been computed
for the arbitrary indices 207/206, and 208/206 shown in Table H. In com¬
puting the averages a few obvious anomalies have been deleted because of
their undue effect on the averages. The anomalies for districts in the
Mississippi Valley have been retained, however, since they constitute the
established pattern for the region. The averages indicated generally reflect
101
the age of mineralization common to the region, excepting of course,
the Mississippi Valley districts. For some of the regions a paucity
of samples requires that 'arger uncertainties be associated with their
averages than for those with a greater number of analyses. With the
averages summarized in Table VII, semi- quantitative criteria are
provided for determining the possible anomalous nature of common leads
from any given region of those listed.
Table VII
Lead Isotopic Averages for Regions in the United States
Region
No. Samples
Sample Nos. of
Anomalies Deleted
Ave rage
207/206
Ave rage
208/206
Rocky Mts .
8
23 - 28
. 8427
2 . 088
Colorado
6
. 8331
2.072
Mississippi Valley
Ill. , la. , Wise.
12
. 7287
1 . 896
South. Ill . , Ky .
2
. 7833
1.994
S . E . Missouri
7
6 5
. 7510
1 . 913
Tri-State Dist.
14
.7311
1 . 887
North Ark.
2
. 7230
1.870
Ky . -Tenn.
4
. 7961
1. 995
Appalachian Mts .
New England
12
96
. 8498
2.088
Penn. , New York
1 1
. 8396
2. 076
Southern
2
. 8690
2.098
Joplin- Type Anomaly
- The Mississippi Valley Leads
An important observation from the data of the present research is that leads
from the whole Mississippi Valley, from the Wisconsin -Illinois - Iowa
district down through the Missouri districts to Northern Arkansas, have the
same anomalous character as the Joplin leads. This is an important fact
which must be embodied in any hypothesis proposed to explain the anomalies.
102
4 l Q
Earlier attempts ’ to account for the character of the Joplin leads
have generally invoked one of the following two factors: (1) a high uranium
and thorium to lead ratio (in effect, anomalous PQ and WQ) in the rock
sources from which the lead was extracted; (2) the presence of radioactive
deposits at depth, which produced radiogenic lead which mixed with the
ore-bearing solutions. The main objection to the fir st hypothe sis is that
the values required for the PQ and WQ anomalies are so large (PQ = 28 and
Wq = 82, for example) that in comparison to values thus far observed in
crustal rocks, they seem unrealistic. In light of the geographically
extended nature of the Joplin-type anomaly as delineated by the isotopic
analyses reported in this work, the second factor suggested must require
either a very extensive deposit of such radioactive minerals, or a large
lateral distance of transport by the ore -carrying solutions, neither of which
seems a likely prospect. It seems more reasonable that differential
extraction of rock lead is involved. This hypothesis will be developed in
the following pages.
103
Geologic Setting
The geology of the ore districts of the Mississippi Valley may be
described in general terms as follows, after Lindgren^ and Behre,
41
Heyl and McKnight . The deposits have no conclusive association
with igneous rocks and characteristically occur in limestones, dolomites,
cherts (derived from limestone), or calcareous shales. Specifically, the
Illinois -Iowa- Wisconsin deposits are found primarily in the Galena dolomite
and the Decorah formation (Ordovician); in southeast Missouri the main
ore-bearing strata are the Bonne-terre and Potosi dolomites of Upper
Cambrian Age; the Boone formation and the Chester group (Mis sissippian
Age) are the main sites of deposition in the Tri-State region. Lead and
zinc are of secondary importance in the fluorite deposits in the southern-
Illinois district and here the mineralization occurs in veins on faults that cut
Mississippian limestones, and in tabular replacement deposits in the same
limestones. The ore -bearing strata are usually capped by shale.
Galena and sphalerite are the essential minerals in the deposits, but
the ore also contains small amounts of nickel, cobalt, iron, copper and
cadmium. With the exception of a small amount of silver found in the upper
Mississippi Valley deposits and in places in the associated fluorite ores in
southern Illinois and locally in the ores of southeastern Missouri, silver
is generally absent. Mineral associations indicate a shallow deposition at
temperatures and pressures comparable to surface conditions. Dikes,
small plugs and sills of basic igneous rocks occur in the southern Illinois-
Kentucky district near the fluorite veins, and are of older age. The only
104
other evidences of adjacent igneous activity are findings of a siliceous
breccia mass cutting Paleozoic rocks in southern Illinois, a granite
intruded into the Paleozoic of Kansas, and a granite of probable
Mesozoic age found at 1250 feet depth in the Bird-Dog Mine, Oklahoma.
The ores are found as irregular deposits near the surface and as
tabular "blanket deposits" at depth, the deepest mines being 300 to 500
feet. The ore may occur disseminated in limestone or dolomite, in
massive replacement deposits along the bedding, as veinlets or small
cavity fillings, in fault breccias and in solution breccias and cavities,
the different types commonly being intermixed. The rock strata tend to
be flat-lying, showing little folding or faulting. Where fault and joint
patterns exist, they control deposition; but deposits are found indepen¬
dent of such patterns. In regions of gentle folding, deposition is con¬
trolled by fracture zones on limbs of the folds; and a tendency to follow
pitching troughs has been observed.
The genesis of the Mississippi valley deposits is still a matter of
controversy. Early opinions favored the Paleozoic sedimentary beds
as the source, with the deposition affected by meteoric waters. Others
have suggested deposition from artesian waters. In more recent years,
the evidence has been interpreted to indicate deposition by hydrothermal
solutions. However, as Behre, Heyl and McKnight point out, no
criteria have yet been discovered that finally substantiate any of these
hypothes es .
General observations as to the nature of the anomaly of the
Mississippi Valley leads, as deduced from the analyses in Table II,
may now be enumerated in the following manner:
(1) As noted previously, the anomalies are characterized
by excess radiogenic content, the excess favoring Pb^^
(2) The amount of radiogenic lead is not only high, but
variably so. The variations are well outside the limits
of experimental uncertainty in the isotopic composition
While the excess may run as high as 20% for Pb^uo, it
is to be noted that for many samples the radiogenic con¬
tent is much lower, and no. 65, from Flat River, Mo. ,
in particular has essentially no excess radiogenic lead
and must be regarded as a normal lead.
(3) The excess radiogenic content is not only variable in
concentration, but also over relatively short distances.
As an illustrative case, the variations of samples 61
through 65--all from one locality, Flat River, Mo. --
may be noted.
It is believed that the second and third observations inparticular ,
argue against the earlier hypotheses which were advanced to explain
the Joplin-type anomaly.
As a preliminary to the detailed presentation of an alternate
hypothesis, the nature of the distribution of lead, uranium and thorium
106
42, 43
in ordinary rocks should be considered. It is well established
that lead, uranium and thorium atoms are distributed throughout the
various mineral grains (or equivalent domains in a non-crystalline
matrix) comprising any given rock; the amounts of the three elements
may not only vary from grain to grain, but any one of the three may
be selectively enriched in one or more mineral species. This fact is
conclusively demonstrated for example in the study of the distribution
44
of lead, uranium, and thorium in the Essonville granite by Tilton ,
et al .
45 45
Of further significance is the discovery by Hurley and Brown
et al. that intergranular surfaces of granite may carry a significant
fraction of the uranium and thorium in the rock. It follows that the
radiogenic lead daughters likewise would be preferentially concentrated
along intergranular surfaces. Qualitatively at least, it appears that a
similar situation would prevail in other igneous and metamorphic rocks
and to a certain extent in sedimentary rocks as well.
On the basis of the observed inhomogeneous distribution of uranium
and thorium in rocks, the following hypothesis is postulated to account
for the Joplin-type anomaly. It is simply that, either in initial extraction
processes or in transit, solutions permeated large volumes of rock con¬
taining inhomogeneously distributed lead under such conditions that only
part of the lead present was removed. As a result the radiogenic lead
was preferentially extracted since it was most accessible to the action
107
of the solutions.
This situation is in marked contrast to that postulated for a normal
lead- -namely, that the lead be extracted uniformly by complete mixing
of the total lead in the rock, and that no extraneous lead be added to the
ore-carrying solutions in transport (see assumptions 7 and 11 on pages
65 and 66). Under low temperature conditions it is evident that with
preferential concentration of radiogenic lead in intergranular regions, a
uniform removal of the total rock lead would not be likely. As for the
matter of transport, it is seen that for the cases where the ore channel
is fairly well restricted, the amount of rock surface exposed to the solu¬
tions is relatively small so that there is little possibility of extraneous
contamination by the process mentioned above.
With such a mechanism for the extraction or addition of inhomo-
geneously distributed lead by low-temperature solutions, a number of
variable factors are at once suggested to account for the variations in
isotopic composition of the mineralized lead, even over short geographic
distances. These variables are enumerated as follows:
(1) Variations in net lead content with rock facies.
(Z) Variations in the extent to which excess radiogenic
lead is concentrated along intergranular boundaries.
(3) Variable lengths of time during which the solutions
are active.
108
(4) Differing temperatures at which the lead is taken
into solution.
(5) Variations in pH and in other properties of the
solutions affecting the solubility of the lead.
(6) Variation in the extent to which a given rock volume
has been "worked" by previous solutions.
(7) For the case of "contamination" of solutions carrying
ore from an original homogeneous source, variations
in the ratio of "contaminating" lead to original lead
due to factors not included in the foregoing.
(8) The presence of radon, with a 3 1/2 day half-life, in
238
the U decay chain may serve to give a selective
mobility to the Pb^ daughter, due to the possibility
of the radon escaping into intergranular regions before
disintegration.
(9) Variations of excess uranium to thorium in the inter¬
granular regions, with resulting differences in the
amounts of the interstitial lead daughters.
It is seen that items (1) through (7) affect the radiogenic isotopes
indiscriminately, whereas factors (8) and (9) may give rise to preferential
effects on the three heavier isotopes. Without detailed knowledge of
109
environments of lead ore genesis, it is difficult to assess the relative
importance of the factors enumerated. However, general considerations
would assign to variables (2), (3), (5), (6), (8) and (9) the greatest probable
effects but not necessarily in the order named.
The simplest mechanism of the proposed hypothesis would involve
incomplete extraction of the lead from a single source; variations in
isotopic composition would arise with the passage of time, the first extrac¬
tions being richest in radiogenic lead. The remaining possibilities are for
ore (normal isotopic composition) carrying solutions to permeate lead¬
bearing strata and to be contaminated with the radiogenic lead most easily
dissolved; or to mingle with other solutions which have previously acquired
an excess of radiogenic lead under conditions of inhomogeneous extraction.
Combinations of the foregoing possibilities may also arise. In any event,
the applicability of the hypothesis to the Mississippi Valley leads seems
favored by the geological evidence in that broad dispersion of the solutions
through rock bodies is indicated by (1) the nature of extensive replacement
ore bodies and of disseminated ore, (2) the fact that ore feeding channels
have not been found, and (3) the presence of impermeable strata usually
marking limits of ore deposition.
It appears that without further data, no conclusive predictions that
could be made on the basis of the proposed hypothesis will solve the matter
of origin of the deposits (hydrothermal, meteoric or artesian). Each of the
110
three cases could involve the production of anomalous leads by the mecha¬
nism hypothesized. These possibilities are briefly outlined below, together
with their probable implications. These in turn may provide a basis for a
more conclusive study of the deposits on a local basis, using isotopic analyses
on samples procured under close geological control.
Case (la). Hydrothermal origin without contamination.
The word hydrothermal as used here refers to the action of hot waters,
but it is not implied that these waters have been derived at higher temperatures
from normal igneous activity. In this latter instances, the contained lead
would probably have been extracted homogeneously and would not show an
anomalous isotopic composition. It is pictured then, that the lead was inhomo-
geneously extracted from fairly deep-seated sources (probably in the crystalline
basement rocks) under hydrothermal conditions such that the radiogenic lead
in intergranular regions most easily entered into solution and gave rise to an
anomalous isotopic composition. There was probably one such major source
associated with each of the main districts, but as a matter of speculation, there
may have been more. The variations in isotopic composition observed over
short geographic distances probably require either multiple sources or multiple
deposition in the sense that the times of extraction from a single source
differed. The latter explanation would assume a continuous process in which
the total available lead was gradually impoverished as to its radiogenic
isotopes due to the preferential removal of the latter. In any event,
Ill
since the ores have come from some distance and in this case are
premised not to be contaminated in transport, it would seem that ore
bodies genetically related would tend to have the same isotopic composi¬
tion. If the path of deposition could be outlined, only a gradual change
in isotopic composition would be expected at most, and a regular trend
from higher radiogenic content with early deposition to lower radiogenic
content with later deposition would be expected if changes in isotopic
composition were found. Mixing of solutions from such sources would
of course complicate the simple pattern outlined.
Case (lb). Hydrothermal origin with contamination.
If the hydrothermal solutions are derived primarily from igneous sources
the resultant homogeneous extraction would yield lead of essentially
"normal" isotopic constitution. These solutions somewhere in their
upward movement could undergo broad diffusion through rock strata,
and in this process would be selectively contaminated by radiogenic lead
from these rocks. Depending on how near these contaminating sources
were to the site of deposition, variations in isotopic composition would
arise over short geographic distances. Introduction of the time element
and other variables previously enumerated would produce similar results
In general, the variations in isotopic composition so produced would not
follow as regular a pattern as suggested for the previous case.
112
Case (2). Meteoric origin. If atmospheric water in percolating down
through rock strata could remove lead in solution, it is evident that
under such low temperature conditions the extraction would very likely
be inhomogenous and an anomalous lead composition would be obtained.
Variations in the isotopic composition would again tend to show an
irregular pattern, depending as they would on the nature of the various
factors affecting solution.
Case (3). Artesian origin. This situation is very similar to Case 2
but with a minor difference. Less random variations in isotopic composi¬
tion might be expected because of greater possibility of mixing through
lateral circulation.
Additional geochemical studies which may contribute to further
evaluation and applicability of the proposed hypothesis are: (1) measure¬
ment of isotopic composition of the sulphur from the various deposits;
(2) study of the distribution of uranium, thorium and lead relative to
granular structure, in sedimentary rocks.
A final point of interest is the apparent age of the source rocks.
If the most contaminated samples of Mississippi Valley lead are used
and the modern isotopic component of ’’average lead" employed to correct
for the rock leads the difference will reflect the Pb^^, pb^^ and Pb^^
207 206
added by the differential extraction process. The ratio Pb /Pb of
this excess radiogenic lead should give an approximation to the age of the
rocks from which this lead was derived. The results are listed in
Table VIII. Thus the age of the source rocks appears to be 2, 000 m.y.
113
Table VIII
Age of Mississippi Valley lead source rocks
(Modern lead as sumed 204=1 . 00 206 = 18.9 207=15.7 208=39.1)
Sample No.
Iowa -Ill. - Wis .
Pb
206
"Excess"
pb207
Pb
208
Exce s s
207 . 206
Pb /Pb
45
3.0
.4
2.8
. 13
46
3. 5
. 5
2.8
. 14
47
2.3
. 3
1.4
. 13
48
3.3
. 4
2.9
. 12
49
3.3
.4
2.9
. 12
50
3.2
.4
2.8
. 125
51
3.2
.45
2.9
. 14
53
3.6
.4
2.9
.11
54
3.8
.45
3.7
. 12
55
3.3
o 3
2.9
. 09
56
3.7
. 5
3.3
. 135
Av.
. 12 d
, Missouri
62
3.4
. 6
3.7
. 18
63
3.3
. 5
3.3
.15
66
3.8
. 3
2.9
.08
. 14 d
;our i -Kansas
-Oklahoma
68
4.2
. 7
3.3
. 165
70
3.4
. 3
1 .4
.09
114
Table VIII (cont'd.)
Sample No.
Pb206
Pb207
Pb208
Pb207/Pb206
souri- Kansas
71
-Oklahoma
3. 5
. 3
1.8
.09
72
3.2
. 2
1.2
. 06
75
3.3
.4
1.6
. 12
77
3.2
. 35
1.5
. 11
78
3.2
. 4
2.9
. 125
79
3.3
. 35
3.0
. 105
80
3.3
.4
2.5
. 12
85
3.8
.45
2.8
. 12
Apparent ag<
Weighted Av.
e of source rocks
. 11 ± .02
0. 12 ± . 01
2, 000 m. y .
115
Although the maximum spread in apparent age from the individual
207/206 ratios ranges from 1200 to 2600 m.y., most of this spread
is no doubt due to experimental uncertainty since the excess radiogenic
207
Pb abundances are not known to better than 2 5%,
Ivigtut Type Anomaly
Although the most reasonable explanation for this type of anomaly
is the origin in an environment of higher Pb/U+Th than "average lead",
another hypothesis based on inhomogeneous lead extraction is possible.
If a given rock mass has been "worked" by solutions under such circum¬
stances that much of the more accessible radiogenic lead has been
removed, there would result a rock mass with a deficiency of radiogenic
lead. If now at some subsequent time the same rock mass is heated to
higher temperatures, any lead homogeneously extracted would be low
in radiogenic lead. Since the fraction of the total lead in a rock that is
in the intergranular spaces is small, it would be impossible by this
mechanism to obtain large "negative" anomalies of the Ivigtut type.
This mechanism appears statistically unlikely.
Additional Possible Factors Affecting Isotopic Composition
Although rigorous conclusions must await controlled sampling, the
analyses in Table II seem to indicate that isotopic composition is not
affected directly by type of mineral, crystal habit, chemical associations,
or the like. The suite of samples nos. 24 through 28 from the Minnie
Moore Mine, Bellevue, Id., exhibits only small variations in isotopic
116
composition, in spite of differences in crystal habit and origin in the
mine. The anglesite and cerussite samples from Tsumeb, S. Africa,
nos. 160 and 161, exhibit very similar chemical compositions; and
note may also be made of the identical isotopic compositions of the
galena and cerussite from Nertschinsk, U.S.S.R., nos. 134 and 135.
The occurrence of lead in two or more different types of minerals in
the same deposit is often due to weathering effects on one original
mineral. There is no reason to suppose that such chemical phenomena
would affect the isotopic composition of the lead,
On the other hand, the galena and cerussite, nos. 114 and 115 from
Franklin, N. J. , show distinctly different compositions. It is concluded
therefore, that differences in isotopic composition with nature of mineral
or mineral association, reflect differences in age or origin of the lead
involved- -the variations in mineral form and environment do not involve
processes which produce appreciable fractionation of the lead isotopes.
An indication that mineral association reflects conditions of lead-
ore genesis with resulting implications for isotopic composition, maybe
found in consideration of the following four samples: no. 39, from Clear
Creek Co., ; no. 82, from Kellogg Mine, Ark., no. 84, from Montgomery
Co., Ark.; and no. 92, from Denboe Pt., Maine. Each of these minerals
is associated with silver, and it is observed moreover, that the isotopic
compositions are consistently normal, i.e., in keeping with their approxi¬
mate geologic age on the basis of the step differentiaticn model. The presence
117
of silver is taken to reflect ore genesis under mesothermal or hypo-
47
thermal conditions. In the light of previous discussion, a more
homogeneous extraction of lead is likely under these conditions of
intermediate to high temperatures „ Consequently, anomalous composi¬
tions due to inhomogeneous extraction of rock lead are not very probable.
The fact of the normal isotopic constitutions of the four argentiferous
samples, especially the two from Arkansas which are not far from
districts showing anomalous leads, is in keeping with these conclusions.
With reference to possible fractionation with crystal growth, the
meager evidence resulting from this work (see samples 62 and 63) is
48
negative. Cannon has reported a 10% variation in isotopic composition
within a single crystal. This crystal exhibited marked zoning however,
and appears to have an unusual origin. There is little reason to suspect
appreciable effects on the isotopic composition of lead due to chemical
fractionation, hence variations within a single crystal indicate changes
in the source of the solutions from which the ore is deposited.
Conclusions
Isotopic analyses of lead minerals of world- wide distribution have
been found generally consistent with their ages of mineralization.
The selected, dated samples treated by least squares analysis on the
basis of the step-differentiation model yield constants consistent with
the concept of lead ore derivation from essentially continental, siliceous
rocks in contrast to extremely deep-seated sources. The age of the
earth's crust obtained by use of meteoritic lead composition in conjunc¬
tion with the step-differentiation model may be questioned in view of
the possibility of continuous differentiation of the earth's outer layers
throughout geologic time. On the basis of this possibility, a continuous
differentiation model has been developed which gives 5. 3 billion years
as the maximum age of the earth (when terrestrial lead had the composi¬
tion of meteoritic lead) and the age of the earth's crust is indicated to be
over a billion years younger.
Probably the most important single factor affecting the validity of
these conclusions is the matter of differentiation early in earth history.
In a secondary way, these results also depend on the full significance of
primordial abundances of the elements observed in meteorites, on the
relation of terrestrial material to meteoritic material, and on the
cosmogony of the solar system in general. Definitive criteria are needed
to establish what conditions of the earth's outer layer constitute the
earliest existence of a crust.
119
It is evident that a larger number of well-dated pre-Cambrian
samples is needed before a highly definitive evaluation of any of the
proposed models can be made. 20 such samples concentrated along
the older end of the time scale would permit a substantial statistical
treatment. An improved precision of the constants would be permitted
thereby and the results obtained would have greater certainty, but are
not expected to differ in kind from those previously derived. It may be
questioned whether a sufficient number of very old, dated samples can
be procured to decide between the continuous differentiation model and
the step-differentiation model on the basis of lead ores alone.
Average isotopic compositions have been tabulated for the major
regions of the United States. Anomalies have been delineated and are
indicated to arise primarily from differences in origin and age of the
lead. A hypothesis of inhomogeneous extraction of lead from original
or contaminating sources has been advanced to account for the Joplin-
type anomaly prevalent in the Mississippi Valley districts. On the basis
of this hypothesis, calculations of the apparent age of the excess radiogenic
lead in these anomalous samples lead to a figure of 2 billion years.
This result argues in favor of extraction from sources below the
sedimentary column in these particular districts.
The possibility of inhomogeneous extraction of certain ions from rock
masses under low temperature conditions is not original with this work,
but has received new corroboration from the nature of the isotopic
analyses of pertinent leads reported herein, on the basis of the assumed
120
hypothesis. While the hypothesis is compatible with the known geology
of the ores involved and with the broad conditions outlined by this
research, further investigation along the lines suggested is needed for
its conclusive evaluation. Such investigation has of necessity been
beyond the scope of the reconnaissance nature of this work.
121
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